diff --git a/tokio/src/io/util/mem.rs b/tokio/src/io/util/mem.rs
index e91a9328b88..05655894816 100644
--- a/tokio/src/io/util/mem.rs
+++ b/tokio/src/io/util/mem.rs
@@ -16,6 +16,14 @@ use std::{
 /// that can be used as in-memory IO types. Writing to one of the pairs will
 /// allow that data to be read from the other, and vice versa.
 ///
+/// # Closing a `DuplexStream`
+///
+/// If one end of the `DuplexStream` channel is dropped, any pending reads on
+/// the other side will continue to read data until the buffer is drained, then
+/// they will signal EOF by returning 0 bytes. Any writes to the other side,
+/// including pending ones (that are waiting for free space in the buffer) will
+/// return `Err(BrokenPipe)` immediately.
+///
 /// # Example
 ///
 /// ```
@@ -134,7 +142,8 @@ impl AsyncWrite for DuplexStream {
 impl Drop for DuplexStream {
     fn drop(&mut self) {
         // notify the other side of the closure
-        self.write.lock().close();
+        self.write.lock().close_write();
+        self.read.lock().close_read();
     }
 }
 
@@ -151,12 +160,21 @@ impl Pipe {
         }
     }
 
-    fn close(&mut self) {
+    fn close_write(&mut self) {
         self.is_closed = true;
+        // needs to notify any readers that no more data will come
         if let Some(waker) = self.read_waker.take() {
             waker.wake();
         }
     }
+
+    fn close_read(&mut self) {
+        self.is_closed = true;
+        // needs to notify any writers that they have to abort
+        if let Some(waker) = self.write_waker.take() {
+            waker.wake();
+        }
+    }
 }
 
 impl AsyncRead for Pipe {
@@ -217,7 +235,7 @@ impl AsyncWrite for Pipe {
         mut self: Pin<&mut Self>,
         _: &mut task::Context<'_>,
     ) -> Poll<std::io::Result<()>> {
-        self.close();
+        self.close_write();
         Poll::Ready(Ok(()))
     }
 }
diff --git a/tokio/tests/io_mem_stream.rs b/tokio/tests/io_mem_stream.rs
index 3335214cb9d..01baa5369c7 100644
--- a/tokio/tests/io_mem_stream.rs
+++ b/tokio/tests/io_mem_stream.rs
@@ -62,6 +62,25 @@ async fn disconnect() {
     t2.await.unwrap();
 }
 
+#[tokio::test]
+async fn disconnect_reader() {
+    let (a, mut b) = duplex(2);
+
+    let t1 = tokio::spawn(async move {
+        // this will block, as not all data fits into duplex
+        b.write_all(b"ping").await.unwrap_err();
+    });
+
+    let t2 = tokio::spawn(async move {
+        // here we drop the reader side, and we expect the writer in the other
+        // task to exit with an error
+        drop(a);
+    });
+
+    t2.await.unwrap();
+    t1.await.unwrap();
+}
+
 #[tokio::test]
 async fn max_write_size() {
     let (mut a, mut b) = duplex(32);
@@ -73,11 +92,11 @@ async fn max_write_size() {
         assert_eq!(n, 4);
     });
 
-    let t2 = tokio::spawn(async move {
-        let mut buf = [0u8; 4];
-        b.read_exact(&mut buf).await.unwrap();
-    });
+    let mut buf = [0u8; 4];
+    b.read_exact(&mut buf).await.unwrap();
 
     t1.await.unwrap();
-    t2.await.unwrap();
+
+    // drop b only after task t1 finishes writing
+    drop(b);
 }