diff --git a/axum/src/serve/mod.rs b/axum/src/serve/mod.rs
index f5d3b129..1bc10c4d 100644
--- a/axum/src/serve/mod.rs
+++ b/axum/src/serve/mod.rs
@@ -267,14 +267,14 @@ where
 
     fn into_future(self) -> Self::IntoFuture {
         private::ServeFuture(Box::pin(async move {
-            self.run().await;
+            do_serve(self.listener, self.make_service, self.signal).await;
             Ok(())
         }))
     }
 }
 
 #[cfg(all(feature = "tokio", any(feature = "http1", feature = "http2")))]
-impl<L, M, S, F> WithGracefulShutdown<L, M, S, F>
+async fn do_serve<L, M, F, S>(mut listener: L, mut make_service: M, signal: F)
 where
     L: Listener,
     L::Addr: Debug,
@@ -284,93 +284,84 @@ where
     S::Future: Send,
     F: Future<Output = ()> + Send + 'static,
 {
-    async fn run(self) {
-        let Self {
-            mut listener,
-            mut make_service,
-            signal,
-            _marker: _,
-        } = self;
+    let (signal_tx, signal_rx) = watch::channel(());
+    tokio::spawn(async move {
+        signal.await;
+        trace!("received graceful shutdown signal. Telling tasks to shutdown");
+        drop(signal_rx);
+    });
+
+    let (close_tx, close_rx) = watch::channel(());
+
+    loop {
+        let (io, remote_addr) = tokio::select! {
+            conn = listener.accept() => conn,
+            _ = signal_tx.closed() => {
+                trace!("signal received, not accepting new connections");
+                break;
+            }
+        };
+
+        let io = TokioIo::new(io);
+
+        trace!("connection {remote_addr:?} accepted");
+
+        poll_fn(|cx| make_service.poll_ready(cx))
+            .await
+            .unwrap_or_else(|err| match err {});
+
+        let tower_service = make_service
+            .call(IncomingStream {
+                io: &io,
+                remote_addr,
+            })
+            .await
+            .unwrap_or_else(|err| match err {})
+            .map_request(|req: Request<Incoming>| req.map(Body::new));
+
+        let hyper_service = TowerToHyperService::new(tower_service);
+
+        let signal_tx = signal_tx.clone();
+
+        let close_rx = close_rx.clone();
 
-        let (signal_tx, signal_rx) = watch::channel(());
         tokio::spawn(async move {
-            signal.await;
-            trace!("received graceful shutdown signal. Telling tasks to shutdown");
-            drop(signal_rx);
-        });
+            #[allow(unused_mut)]
+            let mut builder = Builder::new(TokioExecutor::new());
+            // CONNECT protocol needed for HTTP/2 websockets
+            #[cfg(feature = "http2")]
+            builder.http2().enable_connect_protocol();
 
-        let (close_tx, close_rx) = watch::channel(());
+            let mut conn = pin!(builder.serve_connection_with_upgrades(io, hyper_service));
+            let mut signal_closed = pin!(signal_tx.closed().fuse());
 
-        loop {
-            let (io, remote_addr) = tokio::select! {
-                conn = listener.accept() => conn,
-                _ = signal_tx.closed() => {
-                    trace!("signal received, not accepting new connections");
-                    break;
-                }
-            };
-
-            let io = TokioIo::new(io);
-
-            trace!("connection {remote_addr:?} accepted");
-
-            poll_fn(|cx| make_service.poll_ready(cx))
-                .await
-                .unwrap_or_else(|err| match err {});
-
-            let tower_service = make_service
-                .call(IncomingStream {
-                    io: &io,
-                    remote_addr,
-                })
-                .await
-                .unwrap_or_else(|err| match err {})
-                .map_request(|req: Request<Incoming>| req.map(Body::new));
-
-            let hyper_service = TowerToHyperService::new(tower_service);
-
-            let signal_tx = signal_tx.clone();
-
-            let close_rx = close_rx.clone();
-
-            tokio::spawn(async move {
-                #[allow(unused_mut)]
-                let mut builder = Builder::new(TokioExecutor::new());
-                // CONNECT protocol needed for HTTP/2 websockets
-                #[cfg(feature = "http2")]
-                builder.http2().enable_connect_protocol();
-
-                let mut conn = pin!(builder.serve_connection_with_upgrades(io, hyper_service));
-                let mut signal_closed = pin!(signal_tx.closed().fuse());
-
-                loop {
-                    tokio::select! {
-                        result = conn.as_mut() => {
-                            if let Err(_err) = result {
-                                trace!("failed to serve connection: {_err:#}");
-                            }
-                            break;
-                        }
-                        _ = &mut signal_closed => {
-                            trace!("signal received in task, starting graceful shutdown");
-                            conn.as_mut().graceful_shutdown();
+            loop {
+                tokio::select! {
+                    result = conn.as_mut() => {
+                        if let Err(_err) = result {
+                            trace!("failed to serve connection: {_err:#}");
                         }
+                        break;
+                    }
+                    _ = &mut signal_closed => {
+                        trace!("signal received in task, starting graceful shutdown");
+                        conn.as_mut().graceful_shutdown();
                     }
                 }
+            }
 
-                drop(close_rx);
-            });
-        }
-
-        drop(close_rx);
-        drop(listener);
-
-        trace!(
-            "waiting for {} task(s) to finish",
-            close_tx.receiver_count()
-        );
-        close_tx.closed().await;
+            drop(close_rx);
+        });
     }
+
+    drop(close_rx);
+    drop(listener);
+
+    trace!(
+        "waiting for {} task(s) to finish",
+        close_tx.receiver_count()
+    );
+    close_tx.closed().await;
 }
 
 /// An incoming stream.