diff --git a/web-transport-quiche/src/ez/driver.rs b/web-transport-quiche/src/ez/driver.rs
index 446ef60..594658a 100644
--- a/web-transport-quiche/src/ez/driver.rs
+++ b/web-transport-quiche/src/ez/driver.rs
@@ -36,6 +36,9 @@ pub(super) struct DriverState {
 
     /// The negotiated ALPN protocol, set after the handshake completes.
     alpn: Option<Vec<u8>>,
+
+    /// Wakers waiting for the handshake to complete.
+    handshake_wakers: Vec<Waker>,
 }
 
 impl DriverState {
@@ -58,6 +61,7 @@ impl DriverState {
             bi: DriverOpen::new(next_bi),
             uni: DriverOpen::new(next_uni),
             alpn: None,
+            handshake_wakers: Vec::new(),
         }
     }
 
@@ -78,6 +82,34 @@ impl DriverState {
         self.alpn.as_deref()
     }
 
+    /// Poll for handshake completion.
+    /// Returns Ready once the handshake completes, or if the connection is closed.
+    pub fn poll_handshake(&mut self, waker: &Waker) -> Poll<Result<(), ConnectionError>> {
+        // Check if already established
+        if self.alpn.is_some() {
+            return Poll::Ready(Ok(()));
+        }
+
+        // Check if connection is closed
+        if let Poll::Ready(err) = self.local.poll(waker) {
+            return Poll::Ready(Err(err));
+        }
+        if let Poll::Ready(err) = self.remote.poll(waker) {
+            return Poll::Ready(Err(err));
+        }
+
+        // Wait for handshake
+        self.handshake_wakers.push(waker.clone());
+        Poll::Pending
+    }
+
+    /// Notify all wakers waiting for handshake completion.
+    /// Should be called when the handshake completes.
+    #[must_use = "wake the handshake wakers"]
+    pub fn complete_handshake(&mut self) -> Vec<Waker> {
+        std::mem::take(&mut self.handshake_wakers)
+    }
+
     #[must_use = "wake the driver"]
     pub fn send(&mut self, stream_id: StreamId) -> Option<Waker> {
         if !self.send.insert(stream_id) {
@@ -179,12 +211,17 @@ impl Driver {
     ) -> Result<(), ConnectionError> {
         // Capture the negotiated ALPN protocol.
         let alpn = qconn.application_proto();
-        self.state.lock().alpn = if alpn.is_empty() {
-            None
-        } else {
-            Some(alpn.to_vec())
+        let wakers = {
+            let mut state = self.state.lock();
+            state.alpn = (!alpn.is_empty()).then(|| alpn.to_vec());
+            state.complete_handshake()
         };
 
+        // Wake all tasks waiting for handshake completion.
+        for waker in wakers {
+            waker.wake();
+        }
+
         // Run poll once to advance any pending operations.
         match self.poll(Waker::noop(), qconn) {
             Poll::Ready(Err(e)) => Err(e),
diff --git a/web-transport-quiche/src/ez/server.rs b/web-transport-quiche/src/ez/server.rs
index 8ae57f6..dc5c19e 100644
--- a/web-transport-quiche/src/ez/server.rs
+++ b/web-transport-quiche/src/ez/server.rs
@@ -12,7 +12,9 @@ use rustls_pki_types::{CertificateDer, PrivateKeyDer};
 use crate::ez::tls::{DynamicCertHook, StaticCertHook};
 use crate::ez::DriverState;
 
-use super::{CertResolver, Connection, DefaultMetrics, Driver, Lock, Metrics, Settings};
+use super::{
+    CertResolver, Connection, ConnectionError, DefaultMetrics, Driver, Lock, Metrics, Settings,
+};
 
 /// Used with [ServerBuilder] to require specific parameters.
 #[derive(Default)]
@@ -201,6 +203,7 @@ impl<M: Metrics> ServerBuilder<M, ServerWithListener> {
 /// The peer address is available before calling [Incoming::accept].
 pub struct Incoming {
     connection: Connection,
+    driver: Lock<DriverState>,
 }
 
 impl Incoming {
@@ -209,9 +212,17 @@ impl Incoming {
         self.connection.peer_addr()
     }
 
-    /// Accept the connection, starting the post-handshake driver.
-    pub fn accept(self) -> Connection {
-        self.connection
+    /// Accept the connection, waiting for the TLS handshake to complete.
+    ///
+    /// Returns the connection once the handshake is complete, or an error if the connection
+    /// is closed before the handshake finishes.
+    pub async fn accept(self) -> Result<Connection, ConnectionError> {
+        use std::future::poll_fn;
+
+        // Wait for handshake to complete
+        poll_fn(|cx| self.driver.lock().poll_handshake(cx.waker())).await?;
+
+        Ok(self.connection)
     }
 }
 
@@ -263,8 +274,11 @@ impl<M: Metrics> Server<M> {
             let session = Driver::new(state.clone(), accept_bi.0, accept_uni.0);
 
             let inner = initial.start(session);
-            let connection = Connection::new(inner, state, accept_bi.1, accept_uni.1);
-            let incoming = Incoming { connection };
+            let connection = Connection::new(inner, state.clone(), accept_bi.1, accept_uni.1);
+            let incoming = Incoming {
+                connection,
+                driver: state,
+            };
 
             if accept.send(incoming).await.is_err() {
                 return Ok(());
diff --git a/web-transport-quiche/src/server.rs b/web-transport-quiche/src/server.rs
index f5e2b14..66f7744 100644
--- a/web-transport-quiche/src/server.rs
+++ b/web-transport-quiche/src/server.rs
@@ -12,6 +12,9 @@ pub enum ServerError {
     #[error("io error: {0}")]
     Io(Arc<std::io::Error>),
 
+    #[error("connection error: {0}")]
+    Connection(#[from] ez::ConnectionError),
+
     #[error("settings error: {0}")]
     Settings(#[from] h3::SettingsError),
 
@@ -158,13 +161,15 @@ impl<M: ez::Metrics> Server<M> {
         loop {
             tokio::select! {
                 Some(incoming) = self.inner.accept() => {
-                    let conn = incoming.accept();
-                    self.accept.push(Box::pin(h3::Request::accept(conn)));
+                    self.accept.push(Box::pin(async move {
+                        let conn = incoming.accept().await?;
+                        h3::Request::accept(conn).await
+                    }));
                 }
                 Some(res) = self.accept.next() => {
                     match res {
                         Ok(session) => return Some(session),
-                        Err(err) => tracing::warn!("ignoring failed HTTP/3 handshake: {}", err),
+                        Err(err) => tracing::warn!("ignoring failed handshake: {}", err),
                     }
                 }
                 else => return None,