diff --git a/http2/server.go b/http2/server.go
index e111019..6e2c5b9 100644
--- a/http2/server.go
+++ b/http2/server.go
@@ -1575,6 +1575,12 @@
 		// type PROTOCOL_ERROR."
 		return ConnectionError(ErrCodeProtocol)
 	}
+	// RFC 7540, sec 6.1: If a DATA frame is received whose stream is not in
+	// "open" or "half-closed (local)" state, the recipient MUST respond with a
+	// stream error (Section 5.4.2) of type STREAM_CLOSED.
+	if state == stateClosed {
+		return streamError(id, ErrCodeStreamClosed)
+	}
 	if st == nil || state != stateOpen || st.gotTrailerHeader || st.resetQueued {
 		// This includes sending a RST_STREAM if the stream is
 		// in stateHalfClosedLocal (which currently means that
diff --git a/http2/server_test.go b/http2/server_test.go
index 4e70ac7..6a27c47 100644
--- a/http2/server_test.go
+++ b/http2/server_test.go
@@ -2396,9 +2396,6 @@
 		// it did before.
 		st.writeData(1, true, []byte("foo"))
 
-		// Get our flow control bytes back, since the handler didn't get them.
-		st.wantWindowUpdate(0, uint32(len("foo")))
-
 		// Sent after a peer sends data anyway (admittedly the
 		// previous RST_STREAM might've still been in-flight),
 		// but they'll get the more friendly 'cancel' code