diff --git a/benchmarks/performance-poetry/complex-poetry/src/main/java/com/squareup/benchmarks/performance/complex/poetry/MaybeLoadingGatekeeperWorkflow.kt b/benchmarks/performance-poetry/complex-poetry/src/main/java/com/squareup/benchmarks/performance/complex/poetry/MaybeLoadingGatekeeperWorkflow.kt
index d6c64532e..d434ffc2d 100644
--- a/benchmarks/performance-poetry/complex-poetry/src/main/java/com/squareup/benchmarks/performance/complex/poetry/MaybeLoadingGatekeeperWorkflow.kt
+++ b/benchmarks/performance-poetry/complex-poetry/src/main/java/com/squareup/benchmarks/performance/complex/poetry/MaybeLoadingGatekeeperWorkflow.kt
@@ -17,7 +17,7 @@ typealias IsLoading = Boolean
 
 @OptIn(WorkflowUiExperimentalApi::class)
 class MaybeLoadingGatekeeperWorkflow<T : Any>(
-  private val childWithLoading: Workflow<T, Any, OverviewDetailScreen>,
+  private val childWithLoading: Workflow<T, Any, OverviewDetailScreen<*>>,
   private val childProps: T,
   private val isLoading: Flow<Boolean>
 ) : StatefulWorkflow<Unit, IsLoading, Unit, MayBeLoadingScreen>() {
diff --git a/benchmarks/performance-poetry/complex-poetry/src/main/java/com/squareup/benchmarks/performance/complex/poetry/PerformancePoemWorkflow.kt b/benchmarks/performance-poetry/complex-poetry/src/main/java/com/squareup/benchmarks/performance/complex/poetry/PerformancePoemWorkflow.kt
index 1a33e909f..cd159887f 100644
--- a/benchmarks/performance-poetry/complex-poetry/src/main/java/com/squareup/benchmarks/performance/complex/poetry/PerformancePoemWorkflow.kt
+++ b/benchmarks/performance-poetry/complex-poetry/src/main/java/com/squareup/benchmarks/performance/complex/poetry/PerformancePoemWorkflow.kt
@@ -32,7 +32,6 @@ import com.squareup.workflow1.WorkflowAction
 import com.squareup.workflow1.WorkflowAction.Companion.noAction
 import com.squareup.workflow1.action
 import com.squareup.workflow1.runningWorker
-import com.squareup.workflow1.ui.Screen
 import com.squareup.workflow1.ui.WorkflowUiExperimentalApi
 import com.squareup.workflow1.ui.container.BackStackScreen
 import com.squareup.workflow1.ui.container.toBackStackScreen
@@ -60,7 +59,7 @@ import kotlinx.coroutines.flow.flow
 class PerformancePoemWorkflow(
   private val simulatedPerfConfig: SimulatedPerfConfig = SimulatedPerfConfig.NO_SIMULATED_PERF,
   private val isLoading: MutableStateFlow<Boolean>,
-) : PoemWorkflow, StatefulWorkflow<Poem, State, ClosePoem, OverviewDetailScreen>() {
+) : PoemWorkflow, StatefulWorkflow<Poem, State, ClosePoem, OverviewDetailScreen<*>>() {
 
   sealed class State {
     val isLoading: Boolean = false
@@ -100,7 +99,7 @@ class PerformancePoemWorkflow(
     renderProps: Poem,
     renderState: State,
     context: RenderContext
-  ): OverviewDetailScreen {
+  ): OverviewDetailScreen<*> {
     if (simulatedPerfConfig.simultaneousActions > 0) {
       repeat(simulatedPerfConfig.simultaneousActions) { index ->
         context.runningWorker(
@@ -222,7 +221,7 @@ class PerformancePoemWorkflow(
           }
 
         val stackedStanzas = visibleStanza?.let {
-          (previousStanzas + visibleStanza).toBackStackScreen<Screen>()
+          (previousStanzas + visibleStanza).toBackStackScreen()
         }
 
         val stanzaListOverview =
diff --git a/benchmarks/performance-poetry/complex-poetry/src/main/java/com/squareup/benchmarks/performance/complex/poetry/PerformancePoemsBrowserWorkflow.kt b/benchmarks/performance-poetry/complex-poetry/src/main/java/com/squareup/benchmarks/performance/complex/poetry/PerformancePoemsBrowserWorkflow.kt
index 5d8aa9af5..dd8613cd8 100644
--- a/benchmarks/performance-poetry/complex-poetry/src/main/java/com/squareup/benchmarks/performance/complex/poetry/PerformancePoemsBrowserWorkflow.kt
+++ b/benchmarks/performance-poetry/complex-poetry/src/main/java/com/squareup/benchmarks/performance/complex/poetry/PerformancePoemsBrowserWorkflow.kt
@@ -12,6 +12,7 @@ import com.squareup.benchmarks.performance.complex.poetry.instrumentation.Tracea
 import com.squareup.benchmarks.performance.complex.poetry.instrumentation.asTraceableWorker
 import com.squareup.benchmarks.performance.complex.poetry.views.BlankScreen
 import com.squareup.sample.container.overviewdetail.OverviewDetailScreen
+import com.squareup.sample.container.overviewdetail.plus
 import com.squareup.sample.poetry.ConfigAndPoems
 import com.squareup.sample.poetry.PoemListScreen.Companion.NO_POEM_SELECTED
 import com.squareup.sample.poetry.PoemListWorkflow
@@ -51,7 +52,7 @@ class PerformancePoemsBrowserWorkflow(
   private val isLoading: MutableStateFlow<Boolean>,
 ) :
   PoemsBrowserWorkflow,
-  StatefulWorkflow<ConfigAndPoems, State, Unit, OverviewDetailScreen>() {
+  StatefulWorkflow<ConfigAndPoems, State, Unit, OverviewDetailScreen<*>>() {
 
   sealed class State {
     object Recurse : State()
@@ -88,7 +89,7 @@ class PerformancePoemsBrowserWorkflow(
     renderProps: ConfigAndPoems,
     renderState: State,
     context: RenderContext
-  ): OverviewDetailScreen {
+  ): OverviewDetailScreen<*> {
     when (renderState) {
       is Recurse -> {
         val recursiveChild = PerformancePoemsBrowserWorkflow(
@@ -188,13 +189,13 @@ class PerformancePoemsBrowserWorkflow(
                 }
               }
             }
-            var poems = OverviewDetailScreen(
+            var poems: OverviewDetailScreen<*> = OverviewDetailScreen(
               overviewRendering = BackStackScreen(
                 poemListRendering.copy(selection = renderState.payload)
               )
             )
             if (renderState.payload != NO_POEM_SELECTED) {
-              val poem: OverviewDetailScreen = context.renderChild(
+              val poem = context.renderChild(
                 poemWorkflow,
                 renderProps.second[renderState.payload]
               ) { clearSelection }
@@ -209,7 +210,7 @@ class PerformancePoemsBrowserWorkflow(
                 poemListRendering.copy(selection = renderState.poemIndex)
               )
             )
-            val poem: OverviewDetailScreen = context.renderChild(
+            val poem = context.renderChild(
               poemWorkflow,
               renderProps.second[renderState.poemIndex]
             ) { clearSelection }
diff --git a/benchmarks/performance-poetry/complex-poetry/src/main/java/com/squareup/benchmarks/performance/complex/poetry/views/MayBeLoadingScreen.kt b/benchmarks/performance-poetry/complex-poetry/src/main/java/com/squareup/benchmarks/performance/complex/poetry/views/MayBeLoadingScreen.kt
index 42a9bee0c..3bd6ea3f2 100644
--- a/benchmarks/performance-poetry/complex-poetry/src/main/java/com/squareup/benchmarks/performance/complex/poetry/views/MayBeLoadingScreen.kt
+++ b/benchmarks/performance-poetry/complex-poetry/src/main/java/com/squareup/benchmarks/performance/complex/poetry/views/MayBeLoadingScreen.kt
@@ -8,11 +8,11 @@ import com.squareup.workflow1.ui.container.FullScreenModal
 
 @OptIn(WorkflowUiExperimentalApi::class)
 typealias MayBeLoadingScreen =
-  BodyAndOverlaysScreen<ScrimScreen<OverviewDetailScreen>, FullScreenModal<LoaderSpinner>>
+  BodyAndOverlaysScreen<ScrimScreen<OverviewDetailScreen<*>>, FullScreenModal<LoaderSpinner>>
 
 @OptIn(WorkflowUiExperimentalApi::class)
 fun MayBeLoadingScreen(
-  baseScreen: OverviewDetailScreen,
+  baseScreen: OverviewDetailScreen<*>,
   loaders: List<LoaderSpinner> = emptyList()
 ): MayBeLoadingScreen {
   return BodyAndOverlaysScreen(
diff --git a/samples/containers/android/src/main/java/com/squareup/sample/container/overviewdetail/OverviewDetailContainer.kt b/samples/containers/android/src/main/java/com/squareup/sample/container/overviewdetail/OverviewDetailContainer.kt
index 3034531b7..c6cd6a142 100644
--- a/samples/containers/android/src/main/java/com/squareup/sample/container/overviewdetail/OverviewDetailContainer.kt
+++ b/samples/containers/android/src/main/java/com/squareup/sample/container/overviewdetail/OverviewDetailContainer.kt
@@ -14,6 +14,7 @@ import com.squareup.workflow1.ui.ViewEnvironment
 import com.squareup.workflow1.ui.WorkflowUiExperimentalApi
 import com.squareup.workflow1.ui.WorkflowViewStub
 import com.squareup.workflow1.ui.container.BackStackScreen
+import com.squareup.workflow1.ui.container.plus
 
 /**
  * Displays [OverviewDetailScreen] renderings in either split pane or single pane
@@ -25,7 +26,7 @@ import com.squareup.workflow1.ui.container.BackStackScreen
  * with [OverviewDetailScreen.overviewRendering] as the base of the stack.
  */
 @OptIn(WorkflowUiExperimentalApi::class)
-class OverviewDetailContainer(view: View) : ScreenViewRunner<OverviewDetailScreen> {
+class OverviewDetailContainer(view: View) : ScreenViewRunner<OverviewDetailScreen<*>> {
 
   private val overviewStub: WorkflowViewStub? = view.findViewById(R.id.overview_stub)
   private val detailStub: WorkflowViewStub? = view.findViewById(R.id.detail_stub)
@@ -42,7 +43,7 @@ class OverviewDetailContainer(view: View) : ScreenViewRunner<OverviewDetailScree
   }
 
   override fun showRendering(
-    rendering: OverviewDetailScreen,
+    rendering: OverviewDetailScreen<*>,
     environment: ViewEnvironment
   ) {
     if (singleStub == null) {
@@ -53,7 +54,7 @@ class OverviewDetailContainer(view: View) : ScreenViewRunner<OverviewDetailScree
   }
 
   private fun renderSplitView(
-    rendering: OverviewDetailScreen,
+    rendering: OverviewDetailScreen<*>,
     viewEnvironment: ViewEnvironment
   ) {
     if (rendering.detailRendering == null && rendering.selectDefault != null) {
@@ -81,7 +82,7 @@ class OverviewDetailContainer(view: View) : ScreenViewRunner<OverviewDetailScree
   }
 
   private fun renderSingleView(
-    rendering: OverviewDetailScreen,
+    rendering: OverviewDetailScreen<*>,
     viewEnvironment: ViewEnvironment,
     stub: WorkflowViewStub
   ) {
@@ -92,7 +93,7 @@ class OverviewDetailContainer(view: View) : ScreenViewRunner<OverviewDetailScree
     stub.show(combined, viewEnvironment + Single)
   }
 
-  companion object : ScreenViewFactory<OverviewDetailScreen> by ScreenViewFactory.fromLayout(
+  companion object : ScreenViewFactory<OverviewDetailScreen<*>> by ScreenViewFactory.fromLayout(
     layoutId = R.layout.overview_detail,
     constructor = ::OverviewDetailContainer
   )
diff --git a/samples/containers/android/src/main/java/com/squareup/sample/container/panel/PanelOverlayDialogFactory.kt b/samples/containers/android/src/main/java/com/squareup/sample/container/panel/PanelOverlayDialogFactory.kt
index 417f60aea..de82600bf 100644
--- a/samples/containers/android/src/main/java/com/squareup/sample/container/panel/PanelOverlayDialogFactory.kt
+++ b/samples/containers/android/src/main/java/com/squareup/sample/container/panel/PanelOverlayDialogFactory.kt
@@ -4,7 +4,6 @@ import android.content.Context
 import android.graphics.Rect
 import androidx.appcompat.app.AppCompatDialog
 import com.squareup.sample.container.R
-import com.squareup.workflow1.ui.Screen
 import com.squareup.workflow1.ui.ViewEnvironment
 import com.squareup.workflow1.ui.WorkflowUiExperimentalApi
 import com.squareup.workflow1.ui.container.OverlayDialogFactory
@@ -17,14 +16,14 @@ import kotlin.reflect.KClass
  * Android support for [PanelOverlay].
  */
 @OptIn(WorkflowUiExperimentalApi::class)
-internal object PanelOverlayDialogFactory : OverlayDialogFactory<PanelOverlay<Screen>> {
-  override val type: KClass<in PanelOverlay<Screen>> = PanelOverlay::class
+internal object PanelOverlayDialogFactory : OverlayDialogFactory<PanelOverlay<*>> {
+  override val type: KClass<in PanelOverlay<*>> = PanelOverlay::class
 
   override fun buildDialog(
-    initialRendering: PanelOverlay<Screen>,
+    initialRendering: PanelOverlay<*>,
     initialEnvironment: ViewEnvironment,
     context: Context
-  ): OverlayDialogHolder<PanelOverlay<Screen>> {
+  ): OverlayDialogHolder<PanelOverlay<*>> {
     val dialog = AppCompatDialog(context, R.style.PanelDialog)
 
     val realHolder = dialog.asDialogHolderWithContent(initialRendering, initialEnvironment)
@@ -32,7 +31,7 @@ internal object PanelOverlayDialogFactory : OverlayDialogFactory<PanelOverlay<Sc
     // We replace the default onUpdateBounds function with one that gives the
     // panel a square shape on tablets. See OverlayDialogFactory for more details
     // on the bounds mechanism.
-    return object : OverlayDialogHolder<PanelOverlay<Screen>> by realHolder {
+    return object : OverlayDialogHolder<PanelOverlay<*>> by realHolder {
       override val onUpdateBounds: ((Rect) -> Unit) = { bounds ->
         val refinedBounds: Rect = if (!dialog.context.isTablet) {
           // On a phone, fill the bounds entirely.
diff --git a/samples/containers/common/src/main/java/com/squareup/sample/container/overviewdetail/OverviewDetailScreen.kt b/samples/containers/common/src/main/java/com/squareup/sample/container/overviewdetail/OverviewDetailScreen.kt
index 740c32431..aac9ddbd0 100644
--- a/samples/containers/common/src/main/java/com/squareup/sample/container/overviewdetail/OverviewDetailScreen.kt
+++ b/samples/containers/common/src/main/java/com/squareup/sample/container/overviewdetail/OverviewDetailScreen.kt
@@ -3,6 +3,7 @@ package com.squareup.sample.container.overviewdetail
 import com.squareup.workflow1.ui.Screen
 import com.squareup.workflow1.ui.WorkflowUiExperimentalApi
 import com.squareup.workflow1.ui.container.BackStackScreen
+import com.squareup.workflow1.ui.container.plus
 
 /**
  * Rendering type for overview / detail containers, with [BackStackScreen] in both roles.
@@ -16,14 +17,14 @@ import com.squareup.workflow1.ui.container.BackStackScreen
  * or a null [selectDefault]. **[selectDefault] cannot be a no-op.**
  */
 @OptIn(WorkflowUiExperimentalApi::class)
-class OverviewDetailScreen private constructor(
-  val overviewRendering: BackStackScreen<Screen>,
-  val detailRendering: BackStackScreen<Screen>? = null,
+class OverviewDetailScreen<out T : Screen> private constructor(
+  val overviewRendering: BackStackScreen<T>,
+  val detailRendering: BackStackScreen<T>? = null,
   val selectDefault: (() -> Unit)? = null
 ) : Screen {
   constructor(
-    overviewRendering: BackStackScreen<Screen>,
-    detailRendering: BackStackScreen<Screen>
+    overviewRendering: BackStackScreen<T>,
+    detailRendering: BackStackScreen<T>
   ) : this(overviewRendering, detailRendering, null)
 
   /**
@@ -31,36 +32,18 @@ class OverviewDetailScreen private constructor(
    * that a selection be made to fill a null [detailRendering].
    */
   constructor(
-    overviewRendering: BackStackScreen<Screen>,
+    overviewRendering: BackStackScreen<T>,
     selectDefault: (() -> Unit)? = null
   ) : this(overviewRendering, null, selectDefault)
 
-  operator fun component1(): BackStackScreen<Screen> = overviewRendering
-  operator fun component2(): BackStackScreen<Screen>? = detailRendering
-
-  /**
-   * Returns a new [OverviewDetailScreen] appending the [overviewRendering] and
-   * [detailRendering] of [other] to those of the receiver. If the new screen's
-   * [detailRendering] is `null`, it will have the [selectDefault] function of [other].
-   */
-  operator fun plus(other: OverviewDetailScreen): OverviewDetailScreen {
-    val newOverview = overviewRendering + other.overviewRendering
-    val newDetail = detailRendering
-      ?.let { it + other.detailRendering }
-      ?: other.detailRendering
-
-    return if (newDetail == null) {
-      OverviewDetailScreen(newOverview, other.selectDefault)
-    } else {
-      OverviewDetailScreen(newOverview, newDetail)
-    }
-  }
+  operator fun component1(): BackStackScreen<T> = overviewRendering
+  operator fun component2(): BackStackScreen<T>? = detailRendering
 
   override fun equals(other: Any?): Boolean {
     if (this === other) return true
     if (javaClass != other?.javaClass) return false
 
-    other as OverviewDetailScreen
+    other as OverviewDetailScreen<*>
 
     return overviewRendering == other.overviewRendering &&
       detailRendering == other.detailRendering &&
@@ -80,3 +63,26 @@ class OverviewDetailScreen private constructor(
       "selectDefault=$selectDefault)"
   }
 }
+
+/**
+ * Returns a new [OverviewDetailScreen] appending the
+ * [overviewRendering][OverviewDetailScreen.overviewRendering] and
+ * [detailRendering][OverviewDetailScreen.detailRendering] of [other] to those of the receiver.
+ * If the new screen's `detailRendering` is `null`, it will have the
+ * [selectDefault][OverviewDetailScreen.selectDefault] function of [other].
+ */
+@OptIn(WorkflowUiExperimentalApi::class)
+operator fun <T : Screen> OverviewDetailScreen<T>.plus(
+  other: OverviewDetailScreen<T>
+): OverviewDetailScreen<T> {
+  val newOverview = overviewRendering + other.overviewRendering
+  val newDetail = detailRendering
+    ?.let { it + other.detailRendering }
+    ?: other.detailRendering
+
+  return if (newDetail == null) {
+    OverviewDetailScreen(newOverview, other.selectDefault)
+  } else {
+    OverviewDetailScreen(newOverview, newDetail)
+  }
+}
diff --git a/samples/containers/common/src/main/java/com/squareup/sample/container/panel/PanelOverlay.kt b/samples/containers/common/src/main/java/com/squareup/sample/container/panel/PanelOverlay.kt
index f4de422e8..49f657244 100644
--- a/samples/containers/common/src/main/java/com/squareup/sample/container/panel/PanelOverlay.kt
+++ b/samples/containers/common/src/main/java/com/squareup/sample/container/panel/PanelOverlay.kt
@@ -6,7 +6,7 @@ import com.squareup.workflow1.ui.container.ModalOverlay
 import com.squareup.workflow1.ui.container.ScreenOverlay
 
 @OptIn(WorkflowUiExperimentalApi::class)
-class PanelOverlay<C : Screen>(
+class PanelOverlay<out C : Screen>(
   override val content: C
 ) : ScreenOverlay<C>, ModalOverlay {
   override fun <D : Screen> map(transform: (C) -> D): PanelOverlay<D> =
diff --git a/samples/containers/common/src/test/java/com/squareup/sample/container/overviewdetail/OverviewDetailScreenTest.kt b/samples/containers/common/src/test/java/com/squareup/sample/container/overviewdetail/OverviewDetailScreenTest.kt
index 0a7063665..9d298044f 100644
--- a/samples/containers/common/src/test/java/com/squareup/sample/container/overviewdetail/OverviewDetailScreenTest.kt
+++ b/samples/containers/common/src/test/java/com/squareup/sample/container/overviewdetail/OverviewDetailScreenTest.kt
@@ -8,61 +8,68 @@ import org.junit.Test
 
 @OptIn(WorkflowUiExperimentalApi::class)
 internal class OverviewDetailScreenTest {
-  data class S<T>(val value: T) : Screen
+  data class FooScreen<T>(val value: T) : Screen
+  data class BarScreen<T>(val value: T) : Screen
 
   @Test fun `minimal structure`() {
-    val screen = OverviewDetailScreen(BackStackScreen(S(1)))
-    assertThat(screen.overviewRendering).isEqualTo(BackStackScreen(S(1)))
+    val screen = OverviewDetailScreen(BackStackScreen(FooScreen(1)))
+    assertThat(screen.overviewRendering).isEqualTo(BackStackScreen(FooScreen(1)))
     assertThat(screen.detailRendering).isNull()
     assertThat(screen.selectDefault).isNull()
   }
 
   @Test fun `minimal equality`() {
-    val screen = OverviewDetailScreen(BackStackScreen(S(1)))
-    assertThat(screen).isEqualTo(OverviewDetailScreen(BackStackScreen(S(1))))
-    assertThat(screen).isNotEqualTo(OverviewDetailScreen(BackStackScreen(S(2))))
+    val screen = OverviewDetailScreen(BackStackScreen(FooScreen(1)))
+    assertThat(screen).isEqualTo(OverviewDetailScreen(BackStackScreen(FooScreen(1))))
+    assertThat(screen).isNotEqualTo(OverviewDetailScreen(BackStackScreen(FooScreen(2))))
   }
 
   @Test fun `minimal hash`() {
-    val screen = OverviewDetailScreen(BackStackScreen(S(1)))
-    assertThat(screen.hashCode()).isEqualTo(OverviewDetailScreen(BackStackScreen(S(1))).hashCode())
+    val screen = OverviewDetailScreen(BackStackScreen(FooScreen(1)))
+    assertThat(screen.hashCode()).isEqualTo(
+      OverviewDetailScreen(BackStackScreen(FooScreen(1))).hashCode()
+    )
     assertThat(screen.hashCode())
-      .isNotEqualTo(OverviewDetailScreen(BackStackScreen(S(2))).hashCode())
+      .isNotEqualTo(OverviewDetailScreen(BackStackScreen(FooScreen(2))).hashCode())
   }
 
   @Test fun `combine minimal`() {
-    val left = OverviewDetailScreen(BackStackScreen(S(1), S(2)))
-    val right = OverviewDetailScreen(BackStackScreen(S(11), S(12)))
+    val left = OverviewDetailScreen(BackStackScreen(FooScreen(1), FooScreen(2)))
+    val right = OverviewDetailScreen(BackStackScreen(FooScreen(11), FooScreen(12)))
 
     assertThat(left + right)
-      .isEqualTo(OverviewDetailScreen(BackStackScreen(S(1), S(2), S(11), S(12))))
+      .isEqualTo(
+        OverviewDetailScreen(
+          BackStackScreen(FooScreen(1), FooScreen(2), FooScreen(11), FooScreen(12))
+        )
+      )
   }
 
   @Test fun `full structure`() {
     val screen = OverviewDetailScreen(
-      overviewRendering = BackStackScreen(S(1), S(2)),
-      detailRendering = BackStackScreen(S(3), S(4))
+      overviewRendering = BackStackScreen(FooScreen(1), FooScreen(2)),
+      detailRendering = BackStackScreen(FooScreen(3), FooScreen(4))
     )
 
-    assertThat(screen.overviewRendering).isEqualTo(BackStackScreen(S(1), S(2)))
-    assertThat(screen.detailRendering).isEqualTo(BackStackScreen(S(3), S(4)))
+    assertThat(screen.overviewRendering).isEqualTo(BackStackScreen(FooScreen(1), FooScreen(2)))
+    assertThat(screen.detailRendering).isEqualTo(BackStackScreen(FooScreen(3), FooScreen(4)))
     assertThat(screen.selectDefault).isNull()
   }
 
   @Test fun `full equality`() {
     val screen1 = OverviewDetailScreen(
-      overviewRendering = BackStackScreen(S(1), S(2)),
-      detailRendering = BackStackScreen(S(3), S(4))
+      overviewRendering = BackStackScreen(FooScreen(1), FooScreen(2)),
+      detailRendering = BackStackScreen(FooScreen(3), FooScreen(4))
     )
 
     val screen2 = OverviewDetailScreen(
-      overviewRendering = BackStackScreen(S(1), S(2)),
-      detailRendering = BackStackScreen(S(3), S(4))
+      overviewRendering = BackStackScreen(FooScreen(1), FooScreen(2)),
+      detailRendering = BackStackScreen(FooScreen(3), FooScreen(4))
     )
 
     val screen3 = OverviewDetailScreen(
-      overviewRendering = BackStackScreen(S(1), S(2)),
-      detailRendering = BackStackScreen(S(3), S(4), S(5))
+      overviewRendering = BackStackScreen(FooScreen(1), FooScreen(2)),
+      detailRendering = BackStackScreen(FooScreen(3), FooScreen(4), FooScreen(5))
     )
 
     assertThat(screen1).isEqualTo(screen2)
@@ -71,18 +78,18 @@ internal class OverviewDetailScreenTest {
 
   @Test fun `full hash`() {
     val screen1 = OverviewDetailScreen(
-      overviewRendering = BackStackScreen(S(1), S(2)),
-      detailRendering = BackStackScreen(S(3), S(4))
+      overviewRendering = BackStackScreen(FooScreen(1), FooScreen(2)),
+      detailRendering = BackStackScreen(FooScreen(3), FooScreen(4))
     )
 
     val screen2 = OverviewDetailScreen(
-      overviewRendering = BackStackScreen(S(1), S(2)),
-      detailRendering = BackStackScreen(S(3), S(4))
+      overviewRendering = BackStackScreen(FooScreen(1), FooScreen(2)),
+      detailRendering = BackStackScreen(FooScreen(3), FooScreen(4))
     )
 
     val screen3 = OverviewDetailScreen(
-      overviewRendering = BackStackScreen(S(1), S(2)),
-      detailRendering = BackStackScreen(S(3), S(4), S(5))
+      overviewRendering = BackStackScreen(FooScreen(1), FooScreen(2)),
+      detailRendering = BackStackScreen(FooScreen(3), FooScreen(4), FooScreen(5))
     )
 
     assertThat(screen1.hashCode()).isEqualTo(screen2.hashCode())
@@ -91,18 +98,23 @@ internal class OverviewDetailScreenTest {
 
   @Test fun `combine full`() {
     val left = OverviewDetailScreen(
-      overviewRendering = BackStackScreen(S(1), S(2)),
-      detailRendering = BackStackScreen(S(3), S(4))
+      overviewRendering = BackStackScreen(FooScreen(1), FooScreen(2)),
+      detailRendering = BackStackScreen(FooScreen(3), FooScreen(4))
     )
     val right = OverviewDetailScreen(
-      overviewRendering = BackStackScreen(S(11), S(12)),
-      detailRendering = BackStackScreen(S(13), S(14))
+      overviewRendering = BackStackScreen(FooScreen(11), FooScreen(12)),
+      detailRendering = BackStackScreen(FooScreen(13), FooScreen(14))
     )
 
     assertThat(left + right).isEqualTo(
       OverviewDetailScreen(
-        overviewRendering = BackStackScreen(S(1), S(2), S(11), S(12)),
-        detailRendering = BackStackScreen(S(3), S(4), S(13), S(14))
+        overviewRendering = BackStackScreen(
+          FooScreen(1),
+          FooScreen(2),
+          FooScreen(11),
+          FooScreen(12)
+        ),
+        detailRendering = BackStackScreen(FooScreen(3), FooScreen(4), FooScreen(13), FooScreen(14))
       )
     )
   }
@@ -110,11 +122,11 @@ internal class OverviewDetailScreenTest {
   @Test fun `selectDefault structure`() {
     val selectDefault = {}
     val screen = OverviewDetailScreen(
-      overviewRendering = BackStackScreen(S(1), S(2)),
+      overviewRendering = BackStackScreen(FooScreen(1), FooScreen(2)),
       selectDefault = selectDefault
     )
 
-    assertThat(screen.overviewRendering).isEqualTo(BackStackScreen(S(1), S(2)))
+    assertThat(screen.overviewRendering).isEqualTo(BackStackScreen(FooScreen(1), FooScreen(2)))
     assertThat(screen.detailRendering).isNull()
     assertThat(screen.selectDefault).isEqualTo(selectDefault)
   }
@@ -123,17 +135,17 @@ internal class OverviewDetailScreenTest {
     val selectDefault = {}
 
     val screen1 = OverviewDetailScreen(
-      overviewRendering = BackStackScreen(S(1), S(2)),
+      overviewRendering = BackStackScreen(FooScreen(1), FooScreen(2)),
       selectDefault = selectDefault
     )
 
     val screen2 = OverviewDetailScreen(
-      overviewRendering = BackStackScreen(S(1), S(2)),
+      overviewRendering = BackStackScreen(FooScreen(1), FooScreen(2)),
       selectDefault = selectDefault
     )
 
     val screen3 = OverviewDetailScreen(
-      overviewRendering = BackStackScreen(S(1), S(2)),
+      overviewRendering = BackStackScreen(FooScreen(1), FooScreen(2)),
       selectDefault = {}
     )
 
@@ -145,17 +157,17 @@ internal class OverviewDetailScreenTest {
     val selectDefault = {}
 
     val screen1 = OverviewDetailScreen(
-      overviewRendering = BackStackScreen(S(1), S(2)),
+      overviewRendering = BackStackScreen(FooScreen(1), FooScreen(2)),
       selectDefault = selectDefault
     )
 
     val screen2 = OverviewDetailScreen(
-      overviewRendering = BackStackScreen(S(1), S(2)),
+      overviewRendering = BackStackScreen(FooScreen(1), FooScreen(2)),
       selectDefault = selectDefault
     )
 
     val screen3 = OverviewDetailScreen(
-      overviewRendering = BackStackScreen(S(1), S(2)),
+      overviewRendering = BackStackScreen(FooScreen(1), FooScreen(2)),
       selectDefault = {}
     )
 
@@ -166,20 +178,48 @@ internal class OverviewDetailScreenTest {
   @Test fun `combine selectDefault`() {
     val selectDefaultLeft = {}
     val left = OverviewDetailScreen(
-      overviewRendering = BackStackScreen(S(1), S(2)),
+      overviewRendering = BackStackScreen(FooScreen(1), FooScreen(2)),
       selectDefault = selectDefaultLeft
     )
     val selectDefaultRight = {}
     val right = OverviewDetailScreen(
-      overviewRendering = BackStackScreen(S(11), S(12)),
+      overviewRendering = BackStackScreen(FooScreen(11), FooScreen(12)),
       selectDefault = selectDefaultRight
     )
 
     assertThat(left + right).isEqualTo(
       OverviewDetailScreen(
-        overviewRendering = BackStackScreen(S(1), S(2), S(11), S(12)),
+        overviewRendering = BackStackScreen(
+          FooScreen(1),
+          FooScreen(2),
+          FooScreen(11),
+          FooScreen(12)
+        ),
         selectDefault = selectDefaultRight
       )
     )
   }
+
+  @Test fun `can combine heterogenous content`() {
+    val left = OverviewDetailScreen(
+      overviewRendering = BackStackScreen(FooScreen(1), FooScreen(2)),
+      detailRendering = BackStackScreen(BarScreen(3), BarScreen(4))
+    )
+    val right = OverviewDetailScreen(
+      overviewRendering = BackStackScreen(BarScreen(11), BarScreen(12)),
+      detailRendering = BackStackScreen(FooScreen(13), FooScreen(14))
+    )
+
+    assertThat(left + right).isEqualTo(
+      OverviewDetailScreen(
+        overviewRendering = BackStackScreen(
+          FooScreen(1),
+          FooScreen(2),
+          BarScreen(11),
+          BarScreen(12)
+        ),
+        detailRendering = BackStackScreen(BarScreen(3), BarScreen(4), FooScreen(13), FooScreen(14))
+      )
+    )
+  }
 }
diff --git a/samples/containers/poetry/src/main/java/com/squareup/sample/poetry/PoemWorkflow.kt b/samples/containers/poetry/src/main/java/com/squareup/sample/poetry/PoemWorkflow.kt
index bb4f7e4c3..0fd033997 100644
--- a/samples/containers/poetry/src/main/java/com/squareup/sample/poetry/PoemWorkflow.kt
+++ b/samples/containers/poetry/src/main/java/com/squareup/sample/poetry/PoemWorkflow.kt
@@ -12,6 +12,6 @@ import com.squareup.workflow1.Workflow
  * (Defining this as an interface allows us to use other implementations
  * in other contexts -- check out our :benchmarks module!)
  */
-interface PoemWorkflow : Workflow<Poem, ClosePoem, OverviewDetailScreen> {
+interface PoemWorkflow : Workflow<Poem, ClosePoem, OverviewDetailScreen<*>> {
   object ClosePoem
 }
diff --git a/samples/containers/poetry/src/main/java/com/squareup/sample/poetry/PoemsBrowserWorkflow.kt b/samples/containers/poetry/src/main/java/com/squareup/sample/poetry/PoemsBrowserWorkflow.kt
index bdd03c1ad..64c17c9a3 100644
--- a/samples/containers/poetry/src/main/java/com/squareup/sample/poetry/PoemsBrowserWorkflow.kt
+++ b/samples/containers/poetry/src/main/java/com/squareup/sample/poetry/PoemsBrowserWorkflow.kt
@@ -14,4 +14,4 @@ typealias ConfigAndPoems = Pair<RecursionGraphConfig, List<Poem>>
  * in other contexts -- check out our :benchmarks module!)
  */
 interface PoemsBrowserWorkflow :
-  Workflow<ConfigAndPoems, Unit, OverviewDetailScreen>
+  Workflow<ConfigAndPoems, Unit, OverviewDetailScreen<*>>
diff --git a/samples/containers/poetry/src/main/java/com/squareup/sample/poetry/RealPoemWorkflow.kt b/samples/containers/poetry/src/main/java/com/squareup/sample/poetry/RealPoemWorkflow.kt
index c8a4720c4..17c68bcb4 100644
--- a/samples/containers/poetry/src/main/java/com/squareup/sample/poetry/RealPoemWorkflow.kt
+++ b/samples/containers/poetry/src/main/java/com/squareup/sample/poetry/RealPoemWorkflow.kt
@@ -17,7 +17,6 @@ import com.squareup.workflow1.StatefulWorkflow
 import com.squareup.workflow1.WorkflowAction
 import com.squareup.workflow1.WorkflowAction.Companion.noAction
 import com.squareup.workflow1.parse
-import com.squareup.workflow1.ui.Screen
 import com.squareup.workflow1.ui.WorkflowUiExperimentalApi
 import com.squareup.workflow1.ui.container.BackStackScreen
 import com.squareup.workflow1.ui.container.toBackStackScreen
@@ -26,7 +25,7 @@ import com.squareup.workflow1.ui.container.toBackStackScreen
  * Default implementation of [PoemWorkflow].
  */
 class RealPoemWorkflow : PoemWorkflow,
-  StatefulWorkflow<Poem, SelectedStanza, ClosePoem, OverviewDetailScreen>() {
+  StatefulWorkflow<Poem, SelectedStanza, ClosePoem, OverviewDetailScreen<*>>() {
 
   override fun initialState(
     props: Poem,
@@ -42,7 +41,7 @@ class RealPoemWorkflow : PoemWorkflow,
     renderProps: Poem,
     renderState: SelectedStanza,
     context: RenderContext
-  ): OverviewDetailScreen {
+  ): OverviewDetailScreen<*> {
     val previousStanzas: List<StanzaScreen> =
       if (renderState == NO_SELECTED_STANZA) {
         emptyList()
@@ -73,7 +72,7 @@ class RealPoemWorkflow : PoemWorkflow,
       }
 
     val stackedStanzas = visibleStanza?.let {
-      (previousStanzas + visibleStanza).toBackStackScreen<Screen>()
+      (previousStanzas + visibleStanza).toBackStackScreen()
     }
 
     val stanzaListOverview =
diff --git a/samples/containers/poetry/src/main/java/com/squareup/sample/poetry/RealPoemsBrowserWorkflow.kt b/samples/containers/poetry/src/main/java/com/squareup/sample/poetry/RealPoemsBrowserWorkflow.kt
index 23ec36336..f330af226 100644
--- a/samples/containers/poetry/src/main/java/com/squareup/sample/poetry/RealPoemsBrowserWorkflow.kt
+++ b/samples/containers/poetry/src/main/java/com/squareup/sample/poetry/RealPoemsBrowserWorkflow.kt
@@ -1,6 +1,7 @@
 package com.squareup.sample.poetry
 
 import com.squareup.sample.container.overviewdetail.OverviewDetailScreen
+import com.squareup.sample.container.overviewdetail.plus
 import com.squareup.sample.poetry.PoemListScreen.Companion.NO_POEM_SELECTED
 import com.squareup.sample.poetry.PoemListWorkflow.Props
 import com.squareup.sample.poetry.model.Poem
@@ -23,7 +24,7 @@ typealias SelectedPoem = Int
 class RealPoemsBrowserWorkflow(
   private val poemWorkflow: PoemWorkflow
 ) : PoemsBrowserWorkflow,
-  StatefulWorkflow<ConfigAndPoems, SelectedPoem, Unit, OverviewDetailScreen>() {
+  StatefulWorkflow<ConfigAndPoems, SelectedPoem, Unit, OverviewDetailScreen<*>>() {
 
   override fun initialState(
     props: ConfigAndPoems,
@@ -39,8 +40,8 @@ class RealPoemsBrowserWorkflow(
     renderProps: ConfigAndPoems,
     renderState: SelectedPoem,
     context: RenderContext
-  ): OverviewDetailScreen {
-    val poems: OverviewDetailScreen =
+  ): OverviewDetailScreen<*> {
+    val poems =
       context.renderChild(PoemListWorkflow, Props(poems = renderProps.second)) { selected ->
         choosePoem(
           selected
@@ -52,7 +53,7 @@ class RealPoemsBrowserWorkflow(
     return if (renderState == NO_POEM_SELECTED) {
       poems
     } else {
-      val poem: OverviewDetailScreen =
+      val poem =
         context.renderChild(poemWorkflow, renderProps.second[renderState]) { clearSelection }
       poems + poem
     }
diff --git a/samples/tictactoe/common/src/main/java/com/squareup/sample/authworkflow/AuthWorkflow.kt b/samples/tictactoe/common/src/main/java/com/squareup/sample/authworkflow/AuthWorkflow.kt
index 9ae4f3738..d429f1e86 100644
--- a/samples/tictactoe/common/src/main/java/com/squareup/sample/authworkflow/AuthWorkflow.kt
+++ b/samples/tictactoe/common/src/main/java/com/squareup/sample/authworkflow/AuthWorkflow.kt
@@ -15,7 +15,6 @@ import com.squareup.workflow1.Workflow
 import com.squareup.workflow1.action
 import com.squareup.workflow1.runningWorker
 import com.squareup.workflow1.rx2.asWorker
-import com.squareup.workflow1.ui.Screen
 import com.squareup.workflow1.ui.WorkflowUiExperimentalApi
 import com.squareup.workflow1.ui.container.BackStackScreen
 
@@ -24,7 +23,7 @@ import com.squareup.workflow1.ui.container.BackStackScreen
  * that build on [AuthWorkflow] decoupled from it, for ease of testing.
  */
 @OptIn(WorkflowUiExperimentalApi::class)
-typealias AuthWorkflow = Workflow<Unit, AuthResult, BackStackScreen<Screen>>
+typealias AuthWorkflow = Workflow<Unit, AuthResult, BackStackScreen<*>>
 
 sealed class AuthState {
   internal data class LoginPrompt(val errorMessage: String = "") : AuthState()
@@ -62,7 +61,7 @@ sealed class AuthResult {
  */
 @OptIn(WorkflowUiExperimentalApi::class)
 class RealAuthWorkflow(private val authService: AuthService) : AuthWorkflow,
-  StatefulWorkflow<Unit, AuthState, AuthResult, BackStackScreen<Screen>>() {
+  StatefulWorkflow<Unit, AuthState, AuthResult, BackStackScreen<*>>() {
 
   override fun initialState(
     props: Unit,
@@ -73,7 +72,7 @@ class RealAuthWorkflow(private val authService: AuthService) : AuthWorkflow,
     renderProps: Unit,
     renderState: AuthState,
     context: RenderContext
-  ): BackStackScreen<Screen> = when (renderState) {
+  ): BackStackScreen<*> = when (renderState) {
     is LoginPrompt -> {
       BackStackScreen(
         LoginScreen(
diff --git a/samples/tictactoe/common/src/main/java/com/squareup/sample/mainworkflow/TicTacToeWorkflow.kt b/samples/tictactoe/common/src/main/java/com/squareup/sample/mainworkflow/TicTacToeWorkflow.kt
index 927b1103b..c9d2cbbde 100644
--- a/samples/tictactoe/common/src/main/java/com/squareup/sample/mainworkflow/TicTacToeWorkflow.kt
+++ b/samples/tictactoe/common/src/main/java/com/squareup/sample/mainworkflow/TicTacToeWorkflow.kt
@@ -21,6 +21,7 @@ import com.squareup.workflow1.renderChild
 import com.squareup.workflow1.ui.WorkflowUiExperimentalApi
 import com.squareup.workflow1.ui.container.BackStackScreen
 import com.squareup.workflow1.ui.container.BodyAndOverlaysScreen
+import com.squareup.workflow1.ui.container.plus
 
 /**
  * Application specific root [Workflow], and demonstration of workflow composition.
diff --git a/samples/tictactoe/common/src/test/java/com/squareup/sample/mainworkflow/TicTacToeWorkflowTest.kt b/samples/tictactoe/common/src/test/java/com/squareup/sample/mainworkflow/TicTacToeWorkflowTest.kt
index 3d3bbf706..7ce5d33e6 100644
--- a/samples/tictactoe/common/src/test/java/com/squareup/sample/mainworkflow/TicTacToeWorkflowTest.kt
+++ b/samples/tictactoe/common/src/test/java/com/squareup/sample/mainworkflow/TicTacToeWorkflowTest.kt
@@ -60,8 +60,7 @@ class TicTacToeWorkflowTest {
 
   private data class S<T>(val value: T) : Screen
 
-  private fun authScreen(wrapped: String = DEFAULT_AUTH) =
-    BackStackScreen<Screen>(S(wrapped))
+  private fun authScreen(wrapped: String = DEFAULT_AUTH) = BackStackScreen(S(wrapped))
 
   private val BodyAndOverlaysScreen<ScrimScreen<*>, *>.panels: List<PanelOverlay<*>>
     get() = overlays.mapNotNull { it as? PanelOverlay<*> }
diff --git a/samples/todo-android/app/src/main/java/com/squareup/sample/todo/TodoListsAppWorkflow.kt b/samples/todo-android/app/src/main/java/com/squareup/sample/todo/TodoListsAppWorkflow.kt
index d49b9ad09..f2c8412ec 100644
--- a/samples/todo-android/app/src/main/java/com/squareup/sample/todo/TodoListsAppWorkflow.kt
+++ b/samples/todo-android/app/src/main/java/com/squareup/sample/todo/TodoListsAppWorkflow.kt
@@ -28,7 +28,7 @@ sealed class TodoListsAppState {
  * relationship. See details in the body of the [render] method.
  */
 object TodoListsAppWorkflow :
-  StatefulWorkflow<Unit, TodoListsAppState, Nothing, OverviewDetailScreen>() {
+  StatefulWorkflow<Unit, TodoListsAppState, Nothing, OverviewDetailScreen<*>>() {
   override fun initialState(
     props: Unit,
     snapshot: Snapshot?
@@ -64,7 +64,7 @@ object TodoListsAppWorkflow :
     renderProps: Unit,
     renderState: TodoListsAppState,
     context: RenderContext
-  ): OverviewDetailScreen {
+  ): OverviewDetailScreen<*> {
     val listOfLists: TodoListsScreen = context.renderChild(
       listsWorkflow,
       renderState.lists
diff --git a/workflow-ui/core-android/src/main/java/com/squareup/workflow1/ui/container/FullScreenModalFactory.kt b/workflow-ui/core-android/src/main/java/com/squareup/workflow1/ui/container/FullScreenModalFactory.kt
index ef0cade7f..a72f8a901 100644
--- a/workflow-ui/core-android/src/main/java/com/squareup/workflow1/ui/container/FullScreenModalFactory.kt
+++ b/workflow-ui/core-android/src/main/java/com/squareup/workflow1/ui/container/FullScreenModalFactory.kt
@@ -13,7 +13,7 @@ import com.squareup.workflow1.ui.WorkflowUiExperimentalApi
  * To provide a custom binding for [FullScreenModal], see [OverlayDialogFactoryFinder].
  */
 @WorkflowUiExperimentalApi
-internal class FullScreenModalFactory<C : Screen>() : OverlayDialogFactory<FullScreenModal<C>> {
+internal class FullScreenModalFactory<C : Screen> : OverlayDialogFactory<FullScreenModal<C>> {
   override val type = FullScreenModal::class
 
   override fun buildDialog(
diff --git a/workflow-ui/core-common/api/core-common.api b/workflow-ui/core-common/api/core-common.api
index d0fa3c05e..3709b2775 100644
--- a/workflow-ui/core-common/api/core-common.api
+++ b/workflow-ui/core-common/api/core-common.api
@@ -216,7 +216,6 @@ public final class com/squareup/workflow1/ui/container/BackStackScreen : com/squ
 	public static final field Companion Lcom/squareup/workflow1/ui/container/BackStackScreen$Companion;
 	public fun <init> (Lcom/squareup/workflow1/ui/Screen;Ljava/util/List;)V
 	public fun <init> (Lcom/squareup/workflow1/ui/Screen;[Lcom/squareup/workflow1/ui/Screen;)V
-	public synthetic fun <init> (Ljava/util/List;Lkotlin/jvm/internal/DefaultConstructorMarker;)V
 	public fun asSequence ()Lkotlin/sequences/Sequence;
 	public fun equals (Ljava/lang/Object;)Z
 	public final fun get (I)Lcom/squareup/workflow1/ui/Screen;
@@ -227,7 +226,6 @@ public final class com/squareup/workflow1/ui/container/BackStackScreen : com/squ
 	public synthetic fun map (Lkotlin/jvm/functions/Function1;)Lcom/squareup/workflow1/ui/Container;
 	public fun map (Lkotlin/jvm/functions/Function1;)Lcom/squareup/workflow1/ui/container/BackStackScreen;
 	public final fun mapIndexed (Lkotlin/jvm/functions/Function2;)Lcom/squareup/workflow1/ui/container/BackStackScreen;
-	public final fun plus (Lcom/squareup/workflow1/ui/container/BackStackScreen;)Lcom/squareup/workflow1/ui/container/BackStackScreen;
 	public fun toString ()Ljava/lang/String;
 }
 
@@ -237,6 +235,7 @@ public final class com/squareup/workflow1/ui/container/BackStackScreen$Companion
 }
 
 public final class com/squareup/workflow1/ui/container/BackStackScreenKt {
+	public static final fun plus (Lcom/squareup/workflow1/ui/container/BackStackScreen;Lcom/squareup/workflow1/ui/container/BackStackScreen;)Lcom/squareup/workflow1/ui/container/BackStackScreen;
 	public static final fun toBackStackScreen (Ljava/util/List;)Lcom/squareup/workflow1/ui/container/BackStackScreen;
 	public static final fun toBackStackScreenOrNull (Ljava/util/List;)Lcom/squareup/workflow1/ui/container/BackStackScreen;
 }
diff --git a/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/Container.kt b/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/Container.kt
index 92100388b..cd04934ac 100644
--- a/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/Container.kt
+++ b/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/Container.kt
@@ -7,7 +7,7 @@ import com.squareup.workflow1.ui.Compatible.Companion.keyFor
  *
  * Why two parameter types? The separate [BaseT] type allows implementations
  * and sub-interfaces to constrain the types that [map] is allowed to
- * transform [ContentT] to. E.g., it allows `FooWrapper<S: Screen>` to declare
+ * transform [C] to. E.g., it allows `FooWrapper<S: Screen>` to declare
  * that [map] is only able to transform `S` to other types of `Screen`.
  *
  * @param BaseT the invariant base type of the contents of such a container,
@@ -17,11 +17,11 @@ import com.squareup.workflow1.ui.Compatible.Companion.keyFor
  * is an [Overlay][com.squareup.workflow1.ui.container.Overlay], but it
  * wraps a [Screen].
  *
- * @param ContentT the specific subtype of [BaseT] collected by this [Container].
+ * @param C the specific subtype of [BaseT] collected by this [Container].
  */
 @WorkflowUiExperimentalApi
-public interface Container<BaseT, out ContentT : BaseT> {
-  public fun asSequence(): Sequence<ContentT>
+public interface Container<BaseT, out C : BaseT> {
+  public fun asSequence(): Sequence<C>
 
   /**
    * Returns a [Container] with the [transform]ed contents of the receiver.
@@ -42,7 +42,7 @@ public interface Container<BaseT, out ContentT : BaseT> {
    *    val childBackStackScreen = renderChild(childWorkflow) { ... }
    *    val loggingBackStackScreen = childBackStackScreen.map { LoggingScreen(it) }
    */
-  public fun <ContentU : BaseT> map(transform: (ContentT) -> ContentU): Container<BaseT, ContentU>
+  public fun <D : BaseT> map(transform: (C) -> D): Container<BaseT, D>
 }
 
 /**
@@ -56,8 +56,8 @@ public interface Container<BaseT, out ContentT : BaseT> {
  * provides a convenient default implementation of [compatibilityKey].
  */
 @WorkflowUiExperimentalApi
-public interface Wrapper<BaseT : Any, ContentT : BaseT> : Container<BaseT, ContentT>, Compatible {
-  public val content: ContentT
+public interface Wrapper<BaseT : Any, out C : BaseT> : Container<BaseT, C>, Compatible {
+  public val content: C
 
   /**
    * Default implementation makes this [Wrapper] compatible with others of the same type,
@@ -66,9 +66,9 @@ public interface Wrapper<BaseT : Any, ContentT : BaseT> : Container<BaseT, Conte
   public override val compatibilityKey: String
     get() = keyFor(content, this::class.simpleName ?: "Wrapper")
 
-  public override fun asSequence(): Sequence<ContentT> = sequenceOf(content)
+  public override fun asSequence(): Sequence<C> = sequenceOf(content)
 
-  public override fun <ContentU : BaseT> map(
-    transform: (ContentT) -> ContentU
-  ): Wrapper<BaseT, ContentU>
+  public override fun <D : BaseT> map(
+    transform: (C) -> D
+  ): Wrapper<BaseT, D>
 }
diff --git a/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/NamedScreen.kt b/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/NamedScreen.kt
index 79fc1a808..a20196b95 100644
--- a/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/NamedScreen.kt
+++ b/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/NamedScreen.kt
@@ -8,7 +8,7 @@ package com.squareup.workflow1.ui
  * UI kits are expected to provide handling for this class by default.
  */
 @WorkflowUiExperimentalApi
-public data class NamedScreen<C : Screen>(
+public data class NamedScreen<out C : Screen>(
   override val content: C,
   val name: String
 ) : Screen, Wrapper<Screen, C> {
diff --git a/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/container/BackStackScreen.kt b/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/container/BackStackScreen.kt
index fc6199171..7bd13ad70 100644
--- a/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/container/BackStackScreen.kt
+++ b/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/container/BackStackScreen.kt
@@ -20,7 +20,7 @@ import com.squareup.workflow1.ui.container.BackStackScreen.Companion.fromListOrN
  * @see fromListOrNull
  */
 @WorkflowUiExperimentalApi
-public class BackStackScreen<StackedT : Screen> private constructor(
+public class BackStackScreen<out StackedT : Screen> internal constructor(
   public val frames: List<StackedT>
 ) : Screen, Container<Screen, StackedT> {
   /**
@@ -54,14 +54,6 @@ public class BackStackScreen<StackedT : Screen> private constructor(
 
   public operator fun get(index: Int): StackedT = frames[index]
 
-  public operator fun plus(other: BackStackScreen<StackedT>?): BackStackScreen<StackedT> {
-    return if (other == null) {
-      this
-    } else {
-      BackStackScreen(frames + other.frames)
-    }
-  }
-
   public override fun <StackedU : Screen> map(
     transform: (StackedT) -> StackedU
   ): BackStackScreen<StackedU> {
@@ -111,6 +103,18 @@ public class BackStackScreen<StackedT : Screen> private constructor(
   }
 }
 
+/**
+ * Returns a new [BackStackScreen] with the [BackStackScreen.frames] of [other] added
+ * to those of the receiver. [other] is nullable for convenience when using with
+ * [toBackStackScreenOrNull].
+ */
+@WorkflowUiExperimentalApi
+public operator fun <T : Screen> BackStackScreen<T>.plus(
+  other: BackStackScreen<T>?
+): BackStackScreen<T> {
+  return other?.let { BackStackScreen(frames + it.frames) } ?: this
+}
+
 @WorkflowUiExperimentalApi
 public fun <T : Screen> List<T>.toBackStackScreenOrNull(): BackStackScreen<T>? =
   fromListOrNull(this)
diff --git a/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/container/EnvironmentScreen.kt b/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/container/EnvironmentScreen.kt
index 6b05343e2..c82219d06 100644
--- a/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/container/EnvironmentScreen.kt
+++ b/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/container/EnvironmentScreen.kt
@@ -16,7 +16,7 @@ import com.squareup.workflow1.ui.plus
  * UI kits are expected to provide handling for this class by default.
  */
 @WorkflowUiExperimentalApi
-public class EnvironmentScreen<C : Screen>(
+public class EnvironmentScreen<out C : Screen>(
   public override val content: C,
   public val environment: ViewEnvironment = ViewEnvironment.EMPTY
 ) : Wrapper<Screen, C>, Screen {
diff --git a/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/container/FullScreenModal.kt b/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/container/FullScreenModal.kt
index 24f62a9a6..870d5cbc3 100644
--- a/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/container/FullScreenModal.kt
+++ b/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/container/FullScreenModal.kt
@@ -9,7 +9,7 @@ import com.squareup.workflow1.ui.WorkflowUiExperimentalApi
  * UI kits are expected to provide handling for this class by default.
  */
 @WorkflowUiExperimentalApi
-public class FullScreenModal<C : Screen>(
+public class FullScreenModal<out C : Screen>(
   public override val content: C
 ) : ScreenOverlay<C>, ModalOverlay {
   override fun <D : Screen> map(transform: (C) -> D): FullScreenModal<D> =
diff --git a/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/container/ScreenOverlay.kt b/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/container/ScreenOverlay.kt
index 7d7814d72..bfd9c3e64 100644
--- a/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/container/ScreenOverlay.kt
+++ b/workflow-ui/core-common/src/main/java/com/squareup/workflow1/ui/container/ScreenOverlay.kt
@@ -8,7 +8,7 @@ import com.squareup.workflow1.ui.Wrapper
  * An [Overlay] built around a root [content] [Screen].
  */
 @WorkflowUiExperimentalApi
-public interface ScreenOverlay<ContentT : Screen> : Overlay, Wrapper<Screen, ContentT> {
+public interface ScreenOverlay<out ContentT : Screen> : Overlay, Wrapper<Screen, ContentT> {
   public override val content: ContentT
 
   override fun <ContentU : Screen> map(transform: (ContentT) -> ContentU): ScreenOverlay<ContentU>
diff --git a/workflow-ui/core-common/src/test/java/com/squareup/workflow1/ui/container/BackStackScreenTest.kt b/workflow-ui/core-common/src/test/java/com/squareup/workflow1/ui/container/BackStackScreenTest.kt
index 9d9daff82..93b33d28c 100644
--- a/workflow-ui/core-common/src/test/java/com/squareup/workflow1/ui/container/BackStackScreenTest.kt
+++ b/workflow-ui/core-common/src/test/java/com/squareup/workflow1/ui/container/BackStackScreenTest.kt
@@ -8,82 +8,119 @@ import kotlin.test.assertFailsWith
 
 @OptIn(WorkflowUiExperimentalApi::class)
 internal class BackStackScreenTest {
-  data class S<T>(val value: T) : Screen
+  data class FooScreen<T>(val value: T) : Screen
+  data class BarScreen<T>(val value: T) : Screen
 
   @Test fun `top  is last`() {
-    assertThat(BackStackScreen(S(1), S(2), S(3), S(4)).top).isEqualTo(S(4))
+    assertThat(BackStackScreen(FooScreen(1), FooScreen(2), FooScreen(3), FooScreen(4)).top).isEqualTo(
+      FooScreen(4)
+    )
   }
 
   @Test fun `backstack is all but top`() {
-    assertThat(BackStackScreen(S(1), S(2), S(3), S(4)).backStack)
-      .isEqualTo(listOf(S(1), S(2), S(3)))
+    assertThat(BackStackScreen(FooScreen(1), FooScreen(2), FooScreen(3), FooScreen(4)).backStack)
+      .isEqualTo(listOf(FooScreen(1), FooScreen(2), FooScreen(3)))
   }
 
   @Test fun `get works`() {
-    assertThat(BackStackScreen(S("able"), S("baker"), S("charlie"))[1]).isEqualTo(S("baker"))
+    assertThat(BackStackScreen(FooScreen("able"), FooScreen("baker"), FooScreen("charlie"))[1]).isEqualTo(
+      FooScreen("baker")
+    )
   }
 
   @Test fun `plus another stack`() {
-    assertThat(BackStackScreen(S(1), S(2), S(3)) + BackStackScreen(S(8), S(9), S(0)))
-      .isEqualTo(BackStackScreen(S(1), S(2), S(3), S(8), S(9), S(0)))
+    assertThat(
+      BackStackScreen(FooScreen(1), FooScreen(2), FooScreen(3)) + BackStackScreen(
+        FooScreen(8),
+        FooScreen(9),
+        FooScreen(0)
+      )
+    )
+      .isEqualTo(
+        BackStackScreen(
+          FooScreen(1),
+          FooScreen(2),
+          FooScreen(3),
+          FooScreen(8),
+          FooScreen(9),
+          FooScreen(0)
+        )
+      )
   }
 
   @Test fun `unequal by order`() {
-    assertThat(BackStackScreen(S(1), S(2), S(3)))
-      .isNotEqualTo(BackStackScreen(S(3), S(2), S(1)))
+    assertThat(BackStackScreen(FooScreen(1), FooScreen(2), FooScreen(3)))
+      .isNotEqualTo(BackStackScreen(FooScreen(3), FooScreen(2), FooScreen(1)))
   }
 
   @Test fun `equal have matching hash`() {
-    assertThat(BackStackScreen(S(1), S(2), S(3)).hashCode())
-      .isEqualTo(BackStackScreen(S(1), S(2), S(3)).hashCode())
+    assertThat(BackStackScreen(FooScreen(1), FooScreen(2), FooScreen(3)).hashCode())
+      .isEqualTo(BackStackScreen(FooScreen(1), FooScreen(2), FooScreen(3)).hashCode())
   }
 
   @Test fun `unequal have mismatching hash`() {
-    assertThat(BackStackScreen(S(1), S(2)).hashCode())
-      .isNotEqualTo(BackStackScreen(S(1), S(2), S(3)).hashCode())
+    assertThat(BackStackScreen(FooScreen(1), FooScreen(2)).hashCode())
+      .isNotEqualTo(BackStackScreen(FooScreen(1), FooScreen(2), FooScreen(3)).hashCode())
   }
 
   @Test fun `bottom and rest`() {
     assertThat(
       BackStackScreen.fromList(
-        listOf(element = S(1)) + listOf(S(2), S(3), S(4))
+        listOf(element = FooScreen(1)) + listOf(FooScreen(2), FooScreen(3), FooScreen(4))
       )
-    ).isEqualTo(BackStackScreen(S(1), S(2), S(3), S(4)))
+    ).isEqualTo(BackStackScreen(FooScreen(1), FooScreen(2), FooScreen(3), FooScreen(4)))
   }
 
   @Test fun singleton() {
-    val stack = BackStackScreen(S("hi"))
-    assertThat(stack.top).isEqualTo(S("hi"))
-    assertThat(stack.frames).isEqualTo(listOf(S("hi")))
-    assertThat(stack).isEqualTo(BackStackScreen(S("hi")))
+    val stack = BackStackScreen(FooScreen("hi"))
+    assertThat(stack.top).isEqualTo(FooScreen("hi"))
+    assertThat(stack.frames).isEqualTo(listOf(FooScreen("hi")))
+    assertThat(stack).isEqualTo(BackStackScreen(FooScreen("hi")))
   }
 
   @Test fun map() {
-    assertThat(BackStackScreen(S(1), S(2), S(3)).map { S(it.value * 2) })
-      .isEqualTo(BackStackScreen(S(2), S(4), S(6)))
+    assertThat(
+      BackStackScreen(FooScreen(1), FooScreen(2), FooScreen(3)).map {
+        FooScreen(it.value * 2)
+      }
+    )
+      .isEqualTo(BackStackScreen(FooScreen(2), FooScreen(4), FooScreen(6)))
   }
 
   @Test fun mapIndexed() {
-    val source = BackStackScreen(S("able"), S("baker"), S("charlie"))
-    assertThat(source.mapIndexed { index, frame -> S("$index: ${frame.value}") })
-      .isEqualTo(BackStackScreen(S("0: able"), S("1: baker"), S("2: charlie")))
+    val source = BackStackScreen(FooScreen("able"), FooScreen("baker"), FooScreen("charlie"))
+    assertThat(source.mapIndexed { index, frame -> FooScreen("$index: ${frame.value}") })
+      .isEqualTo(
+        BackStackScreen(FooScreen("0: able"), FooScreen("1: baker"), FooScreen("2: charlie"))
+      )
   }
 
   @Test fun nullFromEmptyList() {
-    assertThat(emptyList<S<*>>().toBackStackScreenOrNull()).isNull()
+    assertThat(emptyList<FooScreen<*>>().toBackStackScreenOrNull()).isNull()
   }
 
   @Test fun throwFromEmptyList() {
-    assertFailsWith<IllegalArgumentException> { emptyList<S<*>>().toBackStackScreen() }
+    assertFailsWith<IllegalArgumentException> { emptyList<FooScreen<*>>().toBackStackScreen() }
   }
 
   @Test fun fromList() {
-    assertThat(listOf(S(1), S(2), S(3)).toBackStackScreen())
-      .isEqualTo(BackStackScreen(S(1), S(2), S(3)))
+    assertThat(listOf(FooScreen(1), FooScreen(2), FooScreen(3)).toBackStackScreen())
+      .isEqualTo(BackStackScreen(FooScreen(1), FooScreen(2), FooScreen(3)))
   }
 
   @Test fun fromListOrNull() {
-    assertThat(listOf(S(1), S(2), S(3)).toBackStackScreenOrNull())
-      .isEqualTo(BackStackScreen(S(1), S(2), S(3)))
+    assertThat(listOf(FooScreen(1), FooScreen(2), FooScreen(3)).toBackStackScreenOrNull())
+      .isEqualTo(BackStackScreen(FooScreen(1), FooScreen(2), FooScreen(3)))
+  }
+
+  /**
+   * To reminds us why we want the `out` in `BackStackScreen<out T : Screen>`.
+   * Without this, using `BackStackScreen<*>` as `RenderingT` is not practical.
+   */
+  @Test fun heterogenousPlusIsTolerable() {
+    val foo = BackStackScreen(FooScreen(1))
+    val bar = BackStackScreen(BarScreen(1))
+    val both = foo + bar
+    assertThat(both).isEqualTo(foo + bar)
   }
 }