diff --git a/src/proxy/h2.rs b/src/proxy/h2.rs
index 63a87a4695..6a82d437cb 100644
--- a/src/proxy/h2.rs
+++ b/src/proxy/h2.rs
@@ -13,7 +13,7 @@
 // limitations under the License.
 
 use crate::copy;
-use bytes::{BufMut, Bytes};
+use bytes::Bytes;
 use futures_core::ready;
 use h2::Reason;
 use std::io::Error;
@@ -85,7 +85,10 @@ pub struct H2StreamWriteHalf {
     _dropped: Option<DropCounter>,
 }
 
-pub struct TokioH2Stream(H2Stream);
+pub struct TokioH2Stream {
+    stream: H2Stream,
+    buf: Bytes,
+}
 
 struct DropCounter {
     // Whether the other end of this shared counter has already dropped.
@@ -144,7 +147,10 @@ impl Drop for DropCounter {
 // then the specific implementation will conflict with the generic one.
 impl TokioH2Stream {
     pub fn new(stream: H2Stream) -> Self {
-        Self(stream)
+        Self {
+            stream,
+            buf: Bytes::new(),
+        }
     }
 }
 
@@ -154,21 +160,21 @@ impl tokio::io::AsyncRead for TokioH2Stream {
         cx: &mut Context<'_>,
         buf: &mut tokio::io::ReadBuf<'_>,
     ) -> Poll<std::io::Result<()>> {
-        let pinned = std::pin::Pin::new(&mut self.0.read);
-        copy::ResizeBufRead::poll_bytes(pinned, cx).map(|r| match r {
-            Ok(bytes) => {
-                if buf.remaining() < bytes.len() {
-                    Err(Error::other(format!(
-                        "kould overflow buffer of with {} remaining",
-                        buf.remaining()
-                    )))
-                } else {
-                    buf.put(bytes);
-                    Ok(())
-                }
-            }
-            Err(e) => Err(e),
-        })
+        // Just return the bytes we have left over and don't poll the stream because
+        // its unclear what to do if there are bytes left over from the previous read, and when we
+        // poll, we get an error.
+        if self.buf.is_empty() {
+            // If we have no unread bytes, we can poll the stream
+            // and fill self.buf with the bytes we read.
+            let pinned = std::pin::Pin::new(&mut self.stream.read);
+            let res = ready!(copy::ResizeBufRead::poll_bytes(pinned, cx))?;
+            self.buf = res;
+        }
+        // Copy as many bytes as we can from self.buf.
+        let cnt = Ord::min(buf.remaining(), self.buf.len());
+        buf.put_slice(&self.buf[..cnt]);
+        self.buf = self.buf.split_off(cnt);
+        Poll::Ready(Ok(()))
     }
 }
 
@@ -178,7 +184,7 @@ impl tokio::io::AsyncWrite for TokioH2Stream {
         cx: &mut Context<'_>,
         buf: &[u8],
     ) -> Poll<Result<usize, tokio::io::Error>> {
-        let pinned = std::pin::Pin::new(&mut self.0.write);
+        let pinned = std::pin::Pin::new(&mut self.stream.write);
         let buf = Bytes::copy_from_slice(buf);
         copy::AsyncWriteBuf::poll_write_buf(pinned, cx, buf)
     }
@@ -187,7 +193,7 @@ impl tokio::io::AsyncWrite for TokioH2Stream {
         mut self: Pin<&mut Self>,
         cx: &mut Context<'_>,
     ) -> Poll<Result<(), std::io::Error>> {
-        let pinned = std::pin::Pin::new(&mut self.0.write);
+        let pinned = std::pin::Pin::new(&mut self.stream.write);
         copy::AsyncWriteBuf::poll_flush(pinned, cx)
     }
 
@@ -195,7 +201,7 @@ impl tokio::io::AsyncWrite for TokioH2Stream {
         mut self: Pin<&mut Self>,
         cx: &mut Context<'_>,
     ) -> Poll<Result<(), std::io::Error>> {
-        let pinned = std::pin::Pin::new(&mut self.0.write);
+        let pinned = std::pin::Pin::new(&mut self.stream.write);
         copy::AsyncWriteBuf::poll_shutdown(pinned, cx)
     }
 }
diff --git a/src/proxy/pool.rs b/src/proxy/pool.rs
index 4b55b9dd6a..d19ef0b419 100644
--- a/src/proxy/pool.rs
+++ b/src/proxy/pool.rs
@@ -594,9 +594,10 @@ mod test {
     }
 
     /// This is really a test for TokioH2Stream, but its nicer here because we have access to
-    /// streams
+    /// streams.
+    /// Most important, we make sure there are no panics.
     #[tokio::test(flavor = "multi_thread", worker_threads = 2)]
-    async fn small_reads() {
+    async fn read_buffering() {
         let (mut pool, srv) = setup_test(3).await;
 
         let key = key(&srv, 2);
@@ -612,13 +613,28 @@ mod test {
         let c = pool.send_request_pooled(&key.clone(), req()).await.unwrap();
         let mut c = TokioH2Stream::new(c);
         c.write_all(b"abcde").await.unwrap();
-        let mut b = [0u8; 0];
-        // Crucially, this should error rather than panic.
-        if let Err(e) = c.read(&mut b).await {
-            assert_eq!(e.kind(), io::ErrorKind::Other);
-        } else {
-            panic!("Should have errored");
-        }
+        let mut b = [0u8; 100];
+        // Properly buffer reads and don't error
+        assert_eq!(c.read(&mut b).await.unwrap(), 8);
+        assert_eq!(&b[..8], b"poolsrv\n"); // this is added by itself
+        assert_eq!(c.read(&mut b[..1]).await.unwrap(), 1);
+        assert_eq!(&b[..1], b"a");
+        assert_eq!(c.read(&mut b[..1]).await.unwrap(), 1);
+        assert_eq!(&b[..1], b"b");
+        assert_eq!(c.read(&mut b[..1]).await.unwrap(), 1);
+        assert_eq!(&b[..1], b"c");
+        assert_eq!(c.read(&mut b).await.unwrap(), 2); // there are only two bytes left
+        assert_eq!(&b[..2], b"de");
+
+        // Once we drop the pool, we should still retained the buffered data,
+        // but then we should error.
+        c.write_all(b"abcde").await.unwrap();
+        assert_eq!(c.read(&mut b[..3]).await.unwrap(), 3);
+        assert_eq!(&b[..3], b"abc");
+        drop(pool);
+        assert_eq!(c.read(&mut b[..2]).await.unwrap(), 2);
+        assert_eq!(&b[..2], b"de");
+        assert!(c.read(&mut b).await.is_err());
     }
 
     #[tokio::test(flavor = "multi_thread", worker_threads = 2)]