diff --git a/neqo-bin/src/server/http09.rs b/neqo-bin/src/server/http09.rs
index 1887e3ac6f..e183a1b045 100644
--- a/neqo-bin/src/server/http09.rs
+++ b/neqo-bin/src/server/http09.rs
@@ -185,7 +185,7 @@ impl HttpServer {
 }
 
 impl super::HttpServer for HttpServer {
-    fn process(&mut self, dgram: Option<Datagram>, now: Instant) -> Output {
+    fn process(&mut self, dgram: Option<Datagram<&[u8]>>, now: Instant) -> Output {
         self.server.process(dgram, now)
     }
 
diff --git a/neqo-bin/src/server/http3.rs b/neqo-bin/src/server/http3.rs
index dfef3f1be4..1d1d7a1cf8 100644
--- a/neqo-bin/src/server/http3.rs
+++ b/neqo-bin/src/server/http3.rs
@@ -80,7 +80,7 @@ impl Display for HttpServer {
 }
 
 impl super::HttpServer for HttpServer {
-    fn process(&mut self, dgram: Option<Datagram>, now: Instant) -> neqo_http3::Output {
+    fn process(&mut self, dgram: Option<Datagram<&[u8]>>, now: Instant) -> neqo_http3::Output {
         self.server.process(dgram, now)
     }
 
diff --git a/neqo-bin/src/server/mod.rs b/neqo-bin/src/server/mod.rs
index 8927890e8e..fc04fa5ad4 100644
--- a/neqo-bin/src/server/mod.rs
+++ b/neqo-bin/src/server/mod.rs
@@ -191,7 +191,7 @@ fn qns_read_response(filename: &str) -> Result<Vec<u8>, io::Error> {
 
 #[allow(clippy::module_name_repetitions)]
 pub trait HttpServer: Display {
-    fn process(&mut self, dgram: Option<Datagram>, now: Instant) -> Output;
+    fn process(&mut self, dgram: Option<Datagram<&[u8]>>, now: Instant) -> Output;
     fn process_events(&mut self, now: Instant);
     fn has_events(&self) -> bool;
 }
@@ -222,8 +222,11 @@ impl ServerRunner {
     }
 
     /// Tries to find a socket, but then just falls back to sending from the first.
-    fn find_socket(&mut self, addr: SocketAddr) -> &mut crate::udp::Socket {
-        let ((_host, first_socket), rest) = self.sockets.split_first_mut().unwrap();
+    fn find_socket(
+        sockets: &mut [(SocketAddr, crate::udp::Socket)],
+        addr: SocketAddr,
+    ) -> &mut crate::udp::Socket {
+        let ((_host, first_socket), rest) = sockets.split_first_mut().unwrap();
         rest.iter_mut()
             .map(|(_host, socket)| socket)
             .find(|socket| {
@@ -235,27 +238,67 @@ impl ServerRunner {
             .unwrap_or(first_socket)
     }
 
-    async fn process(&mut self, mut dgram: Option<Datagram>) -> Result<(), io::Error> {
+    // Free function (i.e. not taking `&mut self: ServerRunner`) to be callable by
+    // `ServerRunner::read_and_process` while holding a reference to
+    // `ServerRunner::recv_buf`.
+    async fn process_inner(
+        server: &mut Box<dyn HttpServer>,
+        timeout: &mut Option<Pin<Box<Sleep>>>,
+        sockets: &mut [(SocketAddr, crate::udp::Socket)],
+        now: &dyn Fn() -> Instant,
+        mut input_dgram: Option<Datagram<&[u8]>>,
+    ) -> Result<(), io::Error> {
         loop {
-            match self.server.process(dgram.take(), (self.now)()) {
+            match server.process(input_dgram.take(), now()) {
                 Output::Datagram(dgram) => {
-                    let socket = self.find_socket(dgram.source());
+                    let socket = Self::find_socket(sockets, dgram.source());
                     socket.writable().await?;
                     socket.send(&dgram)?;
                 }
                 Output::Callback(new_timeout) => {
                     qdebug!("Setting timeout of {:?}", new_timeout);
-                    self.timeout = Some(Box::pin(tokio::time::sleep(new_timeout)));
-                    break;
-                }
-                Output::None => {
+                    *timeout = Some(Box::pin(tokio::time::sleep(new_timeout)));
                     break;
                 }
+                Output::None => break,
             }
         }
         Ok(())
     }
 
+    async fn read_and_process(&mut self, sockets_index: usize) -> Result<(), io::Error> {
+        loop {
+            let (host, socket) = self.sockets.get_mut(sockets_index).unwrap();
+            let Some(input_dgrams) = socket.recv(*host, &mut self.recv_buf)? else {
+                break;
+            };
+
+            for input_dgram in input_dgrams {
+                Self::process_inner(
+                    &mut self.server,
+                    &mut self.timeout,
+                    &mut self.sockets,
+                    &self.now,
+                    Some(input_dgram),
+                )
+                .await?;
+            }
+        }
+
+        Ok(())
+    }
+
+    async fn process(&mut self) -> Result<(), io::Error> {
+        Self::process_inner(
+            &mut self.server,
+            &mut self.timeout,
+            &mut self.sockets,
+            &self.now,
+            None,
+        )
+        .await
+    }
+
     // Wait for any of the sockets to be readable or the timeout to fire.
     async fn ready(&mut self) -> Result<Ready, io::Error> {
         let sockets_ready = select_all(
@@ -278,30 +321,19 @@ impl ServerRunner {
     pub async fn run(mut self) -> Res<()> {
         loop {
             self.server.process_events((self.now)());
-
-            self.process(None).await?;
+            self.process().await?;
 
             if self.server.has_events() {
                 continue;
             }
 
             match self.ready().await? {
-                Ready::Socket(inx) => loop {
-                    let (host, socket) = self.sockets.get_mut(inx).unwrap();
-                    let Some(dgrams) = socket.recv(*host, &mut self.recv_buf)? else {
-                        break;
-                    };
-                    if dgrams.len() == 0 {
-                        break;
-                    }
-                    let dgrams: Vec<Datagram> = dgrams.map(|d| d.to_owned()).collect();
-                    for dgram in dgrams {
-                        self.process(Some(dgram)).await?;
-                    }
-                },
+                Ready::Socket(sockets_index) => {
+                    self.read_and_process(sockets_index).await?;
+                }
                 Ready::Timeout => {
                     self.timeout = None;
-                    self.process(None).await?;
+                    self.process().await?;
                 }
             }
         }