diff --git a/src/body/body.rs b/src/body/body.rs
index 7df87404f6..866fc95657 100644
--- a/src/body/body.rs
+++ b/src/body/body.rs
@@ -389,7 +389,10 @@ impl HttpBody for Body {
                     ping.record_non_data();
                     Poll::Ready(Ok(t))
                 }
-                Err(e) => Poll::Ready(Err(crate::Error::new_h2(e))),
+                Err(e) => match e.reason() {
+                    Some(h2::Reason::NO_ERROR) | Some(h2::Reason::CANCEL) => Poll::Ready(Ok(None)),
+                    reason => Poll::Ready(Err(crate::Error::new_h2(e))),
+                },
             },
             Kind::Chan {
                 ref mut trailers_rx,
diff --git a/tests/client.rs b/tests/client.rs
index a5fc79da8c..9761ed1bee 100644
--- a/tests/client.rs
+++ b/tests/client.rs
@@ -3213,9 +3213,10 @@ mod conn {
     }
 
     #[tokio::test]
-    async fn http2_responds_before_consuming_request_body() {
+    async fn http2_responds_before_consuming_request_body_no_trailers() {
         // Test that a early-response from server works correctly (request body wasn't fully consumed).
         // https://github.com/hyperium/hyper/issues/2872
+        use hyper::body::HttpBody;
         use hyper::service::service_fn;
 
         let _ = pretty_env_logger::try_init();
@@ -3260,11 +3261,118 @@ mod conn {
         let resp = client.send_request(req).await.expect("send_request");
         assert!(resp.status().is_success());
 
-        let body = concat(resp.into_body())
+        let mut body = resp.into_body();
+
+        let data = body
+            .data()
             .await
+            .expect("response has body")
             .expect("get response body with no error");
+        assert_eq!(data.as_ref(), b"No bread for you!");
+
+        let trailers = body
+            .trailers()
+            .await
+            .expect("get response trailers with no error");
+        assert!(trailers.is_none());
+    }
+
+    #[tokio::test]
+    async fn http2_responds_before_consuming_request_body_with_trailers() {
+        // Test that a early-response from server works correctly (request body wasn't fully consumed).
+        // https://github.com/hyperium/hyper/issues/2872
+        use hyper::body::{HttpBody, SizeHint};
+        use hyper::header::{HeaderMap, HeaderValue};
+        use hyper::service::service_fn;
+
+        let _ = pretty_env_logger::try_init();
+
+        /// An `HttpBody` implementation whose `is_end_stream()` will
+        /// return `true` after sending trailers.
+        pub struct TrailersBody(Option<HeaderMap>);
+
+        impl HttpBody for TrailersBody {
+            type Data = bytes::Bytes;
+            type Error = hyper::Error;
+
+            fn poll_data(
+                self: Pin<&mut Self>,
+                _cx: &mut Context<'_>,
+            ) -> Poll<Option<Result<Self::Data, Self::Error>>> {
+                Poll::Ready(None)
+            }
+
+            fn poll_trailers(
+                mut self: Pin<&mut Self>,
+                _cx: &mut Context<'_>,
+            ) -> Poll<Result<Option<HeaderMap>, Self::Error>> {
+                Poll::Ready(Ok(self.0.take()))
+            }
+
+            fn is_end_stream(&self) -> bool {
+                self.0.is_none()
+            }
+
+            fn size_hint(&self) -> SizeHint {
+                SizeHint::with_exact(0)
+            }
+        }
+
+        let listener = TkTcpListener::bind(SocketAddr::from(([127, 0, 0, 1], 0)))
+            .await
+            .unwrap();
+        let addr = listener.local_addr().unwrap();
+
+        // Spawn an HTTP2 server that responds before reading the whole request body.
+        // It's normal case to decline the request due to headers or size of the body.
+        tokio::spawn(async move {
+            let sock = listener.accept().await.unwrap().0;
+            hyper::server::conn::Http::new()
+                .http2_only(true)
+                .serve_connection(
+                    sock,
+                    service_fn(|_req| async move {
+                        let mut trailers = HeaderMap::new();
+                        trailers.insert("grpc", HeaderValue::from_static("0"));
+                        let body = TrailersBody(Some(trailers));
+                        Ok::<_, hyper::Error>(http::Response::new(body))
+                    }),
+                )
+                .await
+                .expect("serve_connection");
+        });
+
+        let io = tcp_connect(&addr).await.expect("tcp connect");
+        let (mut client, conn) = conn::Builder::new()
+            .http2_only(true)
+            .handshake::<_, Body>(io)
+            .await
+            .expect("http handshake");
+
+        tokio::spawn(async move {
+            conn.await.expect("client conn shouldn't error");
+        });
+
+        // Use a channel to keep request stream open
+        let (tx, body) = hyper::Body::channel();
+        let req = Request::post("/a").body(body).unwrap();
+        let resp = client.send_request(req).await.expect("send_request");
+        assert!(resp.status().is_success());
+
+        let mut body = resp.into_body();
+
+        let data = body.data().await;
+        assert!(data.is_none());
+
+        let trailers = body
+            .trailers()
+            .await
+            .expect("get response trailers with no error")
+            .expect("trailers HeaderMaps is present");
 
-        assert_eq!(body.as_ref(), b"No bread for you!");
+        assert_eq!(trailers.len(), 1);
+        assert_eq!(trailers.get("grpc").unwrap(), "0");
+        drop(tx);
     }
 
     #[tokio::test]