diff --git a/http2/server.go b/http2/server.go
index 3c6b90c..f79dbcb 100644
--- a/http2/server.go
+++ b/http2/server.go
@@ -722,9 +722,13 @@
 		sc.idleTimerCh = sc.idleTimer.C
 	}
 
-	var gracefulShutdownCh <-chan struct{}
+	var gracefulShutdownCh chan struct{}
 	if sc.hs != nil {
-		gracefulShutdownCh = h1ServerShutdownChan(sc.hs)
+		ch := h1ServerShutdownChan(sc.hs)
+		if ch != nil {
+			gracefulShutdownCh = make(chan struct{})
+			go sc.awaitGracefulShutdown(ch, gracefulShutdownCh)
+		}
 	}
 
 	go sc.readFrames() // closed by defer sc.conn.Close above
@@ -773,6 +777,14 @@
 	}
 }
 
+func (sc *serverConn) awaitGracefulShutdown(sharedCh <-chan struct{}, privateCh chan struct{}) {
+	select {
+	case <-sc.doneServing:
+	case <-sharedCh:
+		close(privateCh)
+	}
+}
+
 // readPreface reads the ClientPreface greeting from the peer
 // or returns an error on timeout or an invalid greeting.
 func (sc *serverConn) readPreface() error {