diff --git a/Cargo.toml b/Cargo.toml
index d155f64..2dabafe 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -15,9 +15,9 @@ license = "MIT"
 nightly = []
 
 [dependencies]
-futures-channel-preview = "0.3.0-alpha.17"
-futures-core-preview = "0.3.0-alpha.17"
-futures-io-preview = "0.3.0-alpha.17"
+futures-channel-preview = "0.3.0-alpha.18"
+futures-core-preview = "0.3.0-alpha.18"
+futures-io-preview = "0.3.0-alpha.18"
 
 [dev-dependencies]
 criterion = "0.3"
diff --git a/src/pipe/chunked.rs b/src/pipe/chunked.rs
index a1b2b09..5701aec 100644
--- a/src/pipe/chunked.rs
+++ b/src/pipe/chunked.rs
@@ -21,11 +21,14 @@
 //! individual vector to fit larger chunks of bytes that don't already fit.
 
 use futures_channel::mpsc;
-use futures_core::Stream;
+use futures_core::{FusedStream, Stream};
 use futures_io::{AsyncRead, AsyncWrite};
-use std::io::{self, Cursor};
-use std::pin::Pin;
-use std::task::{Context, Poll};
+use std::{
+    io,
+    io::Cursor,
+    pin::Pin,
+    task::{Context, Poll},
+};
 
 /// Create a new chunked pipe with room for a fixed number of chunks.
 ///
@@ -80,15 +83,22 @@ impl AsyncRead for Reader {
         let mut chunk = match self.chunk.take() {
             Some(chunk) => chunk,
 
-            None => match Pin::new(&mut self.buf_stream_rx).poll_next(cx) {
-                // Wait for a new chunk to be delivered.
-                Poll::Pending => return Poll::Pending,
+            None => {
+                // If the stream has terminated, then do not poll it again.
+                if self.buf_stream_rx.is_terminated() {
+                    return Poll::Ready(Ok(0));
+                }
+
+                match Pin::new(&mut self.buf_stream_rx).poll_next(cx) {
+                    // Wait for a new chunk to be delivered.
+                    Poll::Pending => return Poll::Pending,
 
-                // Pipe has closed, so return EOF.
-                Poll::Ready(None) => return Poll::Ready(Ok(0)),
+                    // Pipe has closed, so return EOF.
+                    Poll::Ready(None) => return Poll::Ready(Ok(0)),
 
-                // Accept the new chunk.
-                Poll::Ready(Some(buf)) => buf,
+                    // Accept the new chunk.
+                    Poll::Ready(Some(buf)) => buf,
+                }
             }
         };
 
@@ -228,7 +238,10 @@ mod tests {
             assert_eq!(reader.read(&mut dest).await.unwrap(), 5);
             assert_eq!(&dest, b"hello");
 
-            assert_eq!(reader.read(&mut dest).await.unwrap(), 0);
+            // Continue returning Ok(0) forever.
+            for _ in 0..3 {
+                assert_eq!(reader.read(&mut dest).await.unwrap(), 0);
+            }
         })
     }
 
@@ -241,9 +254,11 @@ mod tests {
 
         drop(reader);
 
-        match writer.write(b"hello").poll_unpin(&mut context) {
-            Poll::Ready(Err(e)) => assert_eq!(e.kind(), io::ErrorKind::BrokenPipe),
-            _ => panic!("expected poll to be ready"),
+        for _ in 0..3 {
+            match writer.write(b"hello").poll_unpin(&mut context) {
+                Poll::Ready(Err(e)) => assert_eq!(e.kind(), io::ErrorKind::BrokenPipe),
+                _ => panic!("expected poll to be ready"),
+            }
         }
     }
 }