diff --git a/src/proto/connection.rs b/src/proto/connection.rs
index f7fc8fcb..7a07001c 100644
--- a/src/proto/connection.rs
+++ b/src/proto/connection.rs
@@ -482,9 +482,11 @@ where
                 // without error
                 //
                 // See https://github.com/hyperium/hyper/issues/3427
-                if self.streams.is_server()
-                    && self.streams.is_buffer_empty()
+                if self.streams.is_buffer_empty()
                     && matches!(kind, io::ErrorKind::UnexpectedEof)
+                    && (self.streams.is_server()
+                        || self.error.as_ref().map(|f| f.reason() == Reason::NO_ERROR)
+                            == Some(true))
                 {
                     *self.state = State::Closed(Reason::NO_ERROR, Initiator::Library);
                     return Ok(());
diff --git a/tests/h2-tests/tests/client_request.rs b/tests/h2-tests/tests/client_request.rs
index 8c991839..c99cc531 100644
--- a/tests/h2-tests/tests/client_request.rs
+++ b/tests/h2-tests/tests/client_request.rs
@@ -1913,6 +1913,8 @@ async fn receive_settings_frame_twice_with_second_one_non_empty() {
     join(srv, h2).await;
 }
 
+// If the server has not sent a go_away message before dropping the connection
+// make sure the UnexpectedEof error is propogated.
 #[tokio::test]
 async fn server_drop_connection_unexpectedly_return_unexpected_eof_err() {
     h2_support::trace_init!();
@@ -1953,6 +1955,44 @@ async fn server_drop_connection_unexpectedly_return_unexpected_eof_err() {
     join(srv, h2).await;
 }
 
+#[tokio::test]
+async fn server_drop_connection_after_go_away() {
+    h2_support::trace_init!();
+    let (io, mut srv) = mock::new();
+
+    let srv = async move {
+        let settings = srv.assert_client_handshake().await;
+        assert_default_settings!(settings);
+        srv.recv_frame(
+            frames::headers(1)
+                .request("GET", "https://http2.akamai.com/")
+                .eos(),
+        )
+        .await;
+        srv.send_frame(frames::go_away(1)).await;
+        tokio::time::sleep(Duration::from_millis(50)).await;
+        srv.close_without_notify();
+    };
+
+    let h2 = async move {
+        let (mut client, h2) = client::handshake(io).await.unwrap();
+        tokio::spawn(async move {
+            let request = Request::builder()
+                .uri("https://http2.akamai.com/")
+                .body(())
+                .unwrap();
+            let _res = client
+                .send_request(request, true)
+                .unwrap()
+                .0
+                .await
+                .expect("request");
+        });
+        let _ = h2.await.unwrap();
+    };
+    join(srv, h2).await;
+}
+
 const SETTINGS: &[u8] = &[0, 0, 0, 4, 0, 0, 0, 0, 0];
 const SETTINGS_ACK: &[u8] = &[0, 0, 0, 4, 1, 0, 0, 0, 0];