diff --git a/neqo-bin/src/client/http09.rs b/neqo-bin/src/client/http09.rs
index 9bdb6dca85..7d30017bb4 100644
--- a/neqo-bin/src/client/http09.rs
+++ b/neqo-bin/src/client/http09.rs
@@ -138,8 +138,12 @@ pub(crate) fn create_client(
 }
 
 impl super::Client for Connection {
-    fn process(&mut self, dgram: Option<&Datagram>, now: Instant) -> Output {
-        self.process(dgram, now)
+    fn process_output(&mut self, now: Instant) -> Output {
+        self.process_output(now)
+    }
+
+    fn process_input(&mut self, dgram: &Datagram, now: Instant) {
+        self.process_input(dgram, now);
     }
 
     fn close<S>(&mut self, now: Instant, app_error: neqo_transport::AppError, msg: S)
diff --git a/neqo-bin/src/client/http3.rs b/neqo-bin/src/client/http3.rs
index c88a8448f6..486992c51d 100644
--- a/neqo-bin/src/client/http3.rs
+++ b/neqo-bin/src/client/http3.rs
@@ -115,8 +115,12 @@ impl super::Client for Http3Client {
         matches!(self.state(), Http3State::Closed(..))
     }
 
-    fn process(&mut self, dgram: Option<&Datagram>, now: Instant) -> Output {
-        self.process(dgram, now)
+    fn process_output(&mut self, now: Instant) -> Output {
+        self.process_output(now)
+    }
+
+    fn process_input(&mut self, dgram: &Datagram, now: Instant) {
+        self.process_input(dgram, now);
     }
 
     fn close<S>(&mut self, now: Instant, app_error: AppError, msg: S)
diff --git a/neqo-bin/src/client/mod.rs b/neqo-bin/src/client/mod.rs
index 81721802e1..7cb7e3c9ef 100644
--- a/neqo-bin/src/client/mod.rs
+++ b/neqo-bin/src/client/mod.rs
@@ -367,7 +367,8 @@ trait Handler {
 
 /// Network client, e.g. [`neqo_transport::Connection`] or [`neqo_http3::Http3Client`].
 trait Client {
-    fn process(&mut self, dgram: Option<&Datagram>, now: Instant) -> Output;
+    fn process_output(&mut self, now: Instant) -> Output;
+    fn process_input(&mut self, dgram: &Datagram, now: Instant);
     fn close<S>(&mut self, now: Instant, app_error: AppError, msg: S)
     where
         S: AsRef<str> + Display;
@@ -404,7 +405,7 @@ impl<'a, H: Handler> Runner<'a, H> {
                     }
                 }
 
-            self.process(None).await?;
+            self.process_output().await?;
 
             if self.client.is_closed() {
                 if self.args.stats {
@@ -414,16 +415,7 @@ impl<'a, H: Handler> Runner<'a, H> {
             }
 
             match ready(self.socket, self.timeout.as_mut()).await? {
-                Ready::Socket => loop {
-                    let dgrams = self.socket.recv(&self.local_addr)?;
-                    if dgrams.is_empty() {
-                        break;
-                    }
-                    for dgram in &dgrams {
-                        self.process(Some(dgram)).await?;
-                    }
-                    self.handler.maybe_key_update(&mut self.client)?;
-                },
+                Ready::Socket => self.process_input().await?,
                 Ready::Timeout => {
                     self.timeout = None;
                 }
@@ -431,9 +423,9 @@ impl<'a, H: Handler> Runner<'a, H> {
         }
     }
 
-    async fn process(&mut self, mut dgram: Option<&Datagram>) -> Result<(), io::Error> {
+    async fn process_output(&mut self) -> Result<(), io::Error> {
         loop {
-            match self.client.process(dgram.take(), Instant::now()) {
+            match self.client.process_output(Instant::now()) {
                 Output::Datagram(dgram) => {
                     self.socket.writable().await?;
                     self.socket.send(dgram)?;
@@ -452,6 +444,21 @@ impl<'a, H: Handler> Runner<'a, H> {
 
         Ok(())
     }
+
+    async fn process_input(&mut self) -> Res<()> {
+        loop {
+            let dgrams = self.socket.recv(&self.local_addr)?;
+            if dgrams.is_empty() {
+                break;
+            }
+            for dgram in &dgrams {
+                self.client.process_input(dgram, Instant::now());
+            }
+            self.handler.maybe_key_update(&mut self.client)?;
+        }
+
+        Ok(())
+    }
 }
 
 fn qlog_new(args: &Args, hostname: &str, cid: &ConnectionId) -> Res<NeqoQlog> {