diff --git a/src/Connection/Internal/Http2ConnectionProcessor.php b/src/Connection/Internal/Http2ConnectionProcessor.php
index 71fe070e..727426c9 100644
--- a/src/Connection/Internal/Http2ConnectionProcessor.php
+++ b/src/Connection/Internal/Http2ConnectionProcessor.php
@@ -1480,7 +1480,11 @@ private function shutdown(?HttpException $reason = null, ?int $lastId = null): v
                 default => null,
             };
 
-            $this->writeFrame(Http2Parser::GOAWAY, data: \pack('NN', 0, $code) . $message)->ignore();
+            // Without active streams nothing else closes the socket, see releaseStream(). Closing it right away
+            // would discard the GOAWAY frame still waiting in the write queue.
+            $this->writeFrame(Http2Parser::GOAWAY, data: \pack('NN', 0, $code) . $message)
+                ->finally($this->socket->close(...))
+                ->ignore();
 
             foreach ($this->streams as $id => $_stream) {
                 $reason ??= $this->makeDefaultShutdownReason();
diff --git a/test/Connection/Http2ConnectionTest.php b/test/Connection/Http2ConnectionTest.php
index 3f4ff6cd..10a751de 100644
--- a/test/Connection/Http2ConnectionTest.php
+++ b/test/Connection/Http2ConnectionTest.php
@@ -591,6 +591,22 @@ public function testServerGoAwayFrame(): void
         }
     }
 
+    public function testCloseWithoutStreamsClosesSocket(): void
+    {
+        $this->connection->close();
+
+        $received = '';
+        while (null !== $chunk = $this->server->read(new TimeoutCancellation(1))) {
+            $received .= $chunk;
+        }
+
+        self::assertTrue($this->client->isClosed());
+        self::assertStringEndsWith(
+            self::packFrame(\pack('NN', 0, Http2Parser::GRACEFUL_SHUTDOWN), Http2Parser::GOAWAY),
+            $received,
+        );
+    }
+
     public function testServerEarlyResponse(): void
     {
         $request = new Request('http://localhost/', 'POST', BufferedContent::fromString(\str_repeat('a', 2 ** 10)));