diff --git a/src/proto/h1/conn.rs b/src/proto/h1/conn.rs
index bcf28d4b69..c8b355cd63 100644
--- a/src/proto/h1/conn.rs
+++ b/src/proto/h1/conn.rs
@@ -655,6 +655,20 @@ where
         }
     }
 
+    /// If the read side can be cheaply drained, do so. Otherwise, close.
+    pub(super) fn poll_drain_or_close_read(&mut self, cx: &mut task::Context<'_>) {
+        let _ = self.poll_read_body(cx);
+
+        // If still in Reading::Body, just give up
+        match self.state.reading {
+            Reading::Init | Reading::KeepAlive => {
+                trace!("body drained");
+                return;
+            }
+            _ => self.close_read(),
+        }
+    }
+
     pub fn close_read(&mut self) {
         self.state.close_read();
     }
diff --git a/src/proto/h1/dispatch.rs b/src/proto/h1/dispatch.rs
index ff5bf01832..84ee412c3c 100644
--- a/src/proto/h1/dispatch.rs
+++ b/src/proto/h1/dispatch.rs
@@ -186,9 +186,9 @@ where
                         Poll::Ready(Err(_canceled)) => {
                             // user doesn't care about the body
                             // so we should stop reading
-                            trace!("body receiver dropped before eof, closing");
-                            self.conn.close_read();
-                            return Poll::Ready(Ok(()));
+                            trace!("body receiver dropped before eof, draining or closing");
+                            self.conn.poll_drain_or_close_read(cx);
+                            continue;
                         }
                     }
                     match self.conn.poll_read_body(cx) {
diff --git a/tests/client.rs b/tests/client.rs
index 0c815ba053..f7db372273 100644
--- a/tests/client.rs
+++ b/tests/client.rs
@@ -967,6 +967,7 @@ mod dispatch_impl {
     use tokio::net::TcpStream;
     use tokio::runtime::Runtime;
 
+    use hyper::body::HttpBody;
     use hyper::client::connect::{Connected, Connection, HttpConnector};
     use hyper::Client;
 
@@ -1574,6 +1575,95 @@ mod dispatch_impl {
         assert_eq!(connects.load(Ordering::Relaxed), 1);
     }
 
+    #[tokio::test]
+    async fn client_keep_alive_eager_when_chunked() {
+        // If a response body has been read to completion, with completion
+        // determined by some other factor, like decompression, and thus
+        // it is in't polled a final time to clear the final 0-len chunk,
+        // try to eagerly clear it so the connection can still be used.
+
+        let _ = pretty_env_logger::try_init();
+        let server = TcpListener::bind("127.0.0.1:0").unwrap();
+        let addr = server.local_addr().unwrap();
+        let connector = DebugConnector::new();
+        let connects = connector.connects.clone();
+
+        let client = Client::builder().build(connector);
+
+        let (tx1, rx1) = oneshot::channel();
+        let (tx2, rx2) = oneshot::channel();
+        thread::spawn(move || {
+            let mut sock = server.accept().unwrap().0;
+            //drop(server);
+            sock.set_read_timeout(Some(Duration::from_secs(5))).unwrap();
+            sock.set_write_timeout(Some(Duration::from_secs(5)))
+                .unwrap();
+            let mut buf = [0; 4096];
+            sock.read(&mut buf).expect("read 1");
+            sock.write_all(
+                b"\
+                HTTP/1.1 200 OK\r\n\
+                transfer-encoding: chunked\r\n\
+                \r\n\
+                5\r\n\
+                hello\r\n\
+                0\r\n\r\n\
+            ",
+            )
+            .expect("write 1");
+            let _ = tx1.send(());
+
+            let n2 = sock.read(&mut buf).expect("read 2");
+            assert_ne!(n2, 0, "bytes of second request");
+            let second_get = "GET /b HTTP/1.1\r\n";
+            assert_eq!(s(&buf[..second_get.len()]), second_get);
+            sock.write_all(b"HTTP/1.1 200 OK\r\nContent-Length: 0\r\n\r\n")
+                .expect("write 2");
+            let _ = tx2.send(());
+        });
+
+        assert_eq!(connects.load(Ordering::SeqCst), 0);
+
+        let rx = rx1.expect("thread panicked");
+        let req = Request::builder()
+            .uri(&*format!("http://{}/a", addr))
+            .body(Body::empty())
+            .unwrap();
+        let fut = client.request(req);
+
+        let mut resp = future::join(fut, rx).map(|r| r.0).await.unwrap();
+        assert_eq!(connects.load(Ordering::SeqCst), 1);
+        assert_eq!(resp.status(), 200);
+        assert_eq!(resp.headers()["transfer-encoding"], "chunked");
+
+        // Read the "hello" chunk...
+        let chunk = resp.body_mut().data().await.unwrap().unwrap();
+        assert_eq!(chunk, "hello");
+
+        // With our prior knowledge, we know that's the end of the body.
+        // So just drop the body, without polling for the `0\r\n\r\n` end.
+        drop(resp);
+
+        // sleep real quick to let the threadpool put connection in ready
+        // state and back into client pool
+        tokio::time::delay_for(Duration::from_millis(50)).await;
+
+        let rx = rx2.expect("thread panicked");
+        let req = Request::builder()
+            .uri(&*format!("http://{}/b", addr))
+            .body(Body::empty())
+            .unwrap();
+        let fut = client.request(req);
+        future::join(fut, rx).map(|r| r.0).await.unwrap();
+
+        assert_eq!(
+            connects.load(Ordering::SeqCst),
+            1,
+            "second request should still only have 1 connect"
+        );
+        drop(client);
+    }
+
     #[test]
     fn connect_proxy_sends_absolute_uri() {
         let _ = pretty_env_logger::try_init();