diff --git a/muted-tests.yml b/muted-tests.yml
index e1612b941fc06..d4d1e4dfbc6ec 100644
--- a/muted-tests.yml
+++ b/muted-tests.yml
@@ -444,9 +444,6 @@ tests:
 - class: org.elasticsearch.xpack.esql.qa.mixed.EsqlClientYamlIT
   method: test {p0=esql/120_profile/avg 8.14 or after}
   issue: https://github.com/elastic/elasticsearch/issues/127879
-- class: org.elasticsearch.indices.stats.IndexStatsIT
-  method: testThrottleStats
-  issue: https://github.com/elastic/elasticsearch/issues/126359
 - class: org.elasticsearch.search.vectors.IVFKnnFloatVectorQueryTests
   method: testRandomWithFilter
   issue: https://github.com/elastic/elasticsearch/issues/127963
diff --git a/server/src/main/java/org/elasticsearch/index/engine/Engine.java b/server/src/main/java/org/elasticsearch/index/engine/Engine.java
index de8bfd0e3e61c..19c4ef852286e 100644
--- a/server/src/main/java/org/elasticsearch/index/engine/Engine.java
+++ b/server/src/main/java/org/elasticsearch/index/engine/Engine.java
@@ -612,7 +612,6 @@ public Condition newCondition() {
         }
 
         public void throttle() {
-            assert semaphore.availablePermits() == Integer.MAX_VALUE;
             semaphore.acquireUninterruptibly(Integer.MAX_VALUE - allowThreads);
         }
 
diff --git a/server/src/test/java/org/elasticsearch/index/engine/InternalEngineTests.java b/server/src/test/java/org/elasticsearch/index/engine/InternalEngineTests.java
index bc63ef763ec57..f52e753a5ad9f 100644
--- a/server/src/test/java/org/elasticsearch/index/engine/InternalEngineTests.java
+++ b/server/src/test/java/org/elasticsearch/index/engine/InternalEngineTests.java
@@ -162,6 +162,7 @@
 import java.util.concurrent.BrokenBarrierException;
 import java.util.concurrent.CountDownLatch;
 import java.util.concurrent.CyclicBarrier;
+import java.util.concurrent.Executors;
 import java.util.concurrent.Phaser;
 import java.util.concurrent.Semaphore;
 import java.util.concurrent.TimeUnit;
@@ -7686,6 +7687,23 @@ public void testDisableRecoverySource() throws Exception {
         }
     }
 
+    public void testPauseLockCanBeThrottledConcurrently() throws Exception {
+        int allowThreads = randomIntBetween(2, 8);
+        var pauseLock = new Engine.PauseLock(allowThreads);
+        var executor = Executors.newFixedThreadPool(allowThreads);
+        var barrier = new CyclicBarrier(allowThreads);
+        for (int i = 0; i < allowThreads; i++) {
+            executor.submit(() -> {
+                safeAwait(barrier);
+                pauseLock.throttle();
+                pauseLock.unthrottle();
+            });
+        }
+
+        executor.shutdown();
+        assertTrue(executor.awaitTermination(10, TimeUnit.SECONDS));
+    }
+
     private static void assertCommitGenerations(Map<IndexCommit, Engine.IndexCommitRef> commits, List<Long> expectedGenerations) {
         assertCommitGenerations(commits.values().stream().map(Engine.IndexCommitRef::getIndexCommit).toList(), expectedGenerations);
     }