diff --git a/yggquic.go b/yggquic.go
index 73b0495..fffb8b7 100644
--- a/yggquic.go
+++ b/yggquic.go
@@ -24,17 +24,24 @@ import (
 )
 
 type YggdrasilTransport struct {
-	yggdrasil  net.PacketConn
-	listener   *quic.Listener
-	transport  *quic.Transport
-	tlsConfig  *tls.Config
-	quicConfig *quic.Config
-	incoming   chan *yggdrasilSession
-	sessions   sync.Map // string -> quic.Connection
-	dials      sync.Map // string -> *yggdrasilDial
+	yggdrasil   net.PacketConn
+	listener    *quic.Listener
+	transport   *quic.Transport
+	tlsConfig   *tls.Config
+	quicConfig  *quic.Config
+	incoming    chan *yggdrasilStream
+	connections sync.Map // string -> *yggdrasilConnection
+	dials       sync.Map // string -> *yggdrasilDial
 }
 
-type yggdrasilSession struct {
+type yggdrasilConnection struct {
+	context.Context
+	context.CancelFunc
+	quic.Connection
+	done chan struct{}
+}
+
+type yggdrasilStream struct {
 	quic.Connection
 	quic.Stream
 }
@@ -44,22 +51,25 @@ type yggdrasilDial struct {
 	context.CancelFunc
 }
 
-func New(ygg *core.Core, cert tls.Certificate) (*YggdrasilTransport, error) {
+func New(ygg *core.Core, cert tls.Certificate, qc *quic.Config) (*YggdrasilTransport, error) {
+	if qc == nil {
+		qc = &quic.Config{
+			HandshakeIdleTimeout: time.Second * 5,
+			MaxIdleTimeout:       time.Second * 60,
+		}
+	}
 	tr := &YggdrasilTransport{
 		tlsConfig: &tls.Config{
 			ServerName:         hex.EncodeToString(ygg.PublicKey()),
 			Certificates:       []tls.Certificate{cert},
 			InsecureSkipVerify: true,
 		},
-		quicConfig: &quic.Config{
-			HandshakeIdleTimeout: time.Second * 5,
-			MaxIdleTimeout:       time.Second * 60,
-		},
+		quicConfig: qc,
 		transport: &quic.Transport{
 			Conn: ygg,
 		},
 		yggdrasil: ygg,
-		incoming:  make(chan *yggdrasilSession, 1),
+		incoming:  make(chan *yggdrasilStream),
 	}
 
 	var err error
@@ -67,44 +77,58 @@ func New(ygg *core.Core, cert tls.Certificate) (*YggdrasilTransport, error) {
 		return nil, fmt.Errorf("quic.Listen: %w", err)
 	}
 
-	go tr.connectionAcceptLoop()
+	go tr.connectionAcceptLoop(context.TODO())
 	return tr, nil
 }
 
-func (t *YggdrasilTransport) connectionAcceptLoop() {
+func (t *YggdrasilTransport) connectionAcceptLoop(ctx context.Context) {
 	for {
-		qc, err := t.listener.Accept(context.TODO())
+		qc, err := t.listener.Accept(ctx)
 		if err != nil {
 			return
 		}
 
+		// If there's already an open connection for this node then we
+		// will want to shut down the existing one and replace it with
+		// this one.
 		host := qc.RemoteAddr().String()
-		if eqc, ok := t.sessions.LoadAndDelete(host); ok {
-			eqc := eqc.(quic.Connection)
-			_ = eqc.CloseWithError(0, "Connection replaced")
+		ctx, cancel := context.WithCancel(ctx)
+		yc := &yggdrasilConnection{ctx, cancel, qc, make(chan struct{})}
+		if eqc, ok := t.connections.Swap(host, yc); ok {
+			if eqc, ok := eqc.(*yggdrasilConnection); ok {
+				eqc.CancelFunc()
+			}
 		}
-		t.sessions.Store(host, qc)
+
+		// Now if there are any in-progress dials, we can cancel those
+		// too as we now have an open connection that we can open new
+		// streams on.
 		if dial, ok := t.dials.LoadAndDelete(host); ok {
 			dial := dial.(*yggdrasilDial)
 			dial.CancelFunc()
 		}
 
-		go t.streamAcceptLoop(qc)
+		go t.streamAcceptLoop(yc)
 	}
 }
 
-func (t *YggdrasilTransport) streamAcceptLoop(qc quic.Connection) {
-	host := qc.RemoteAddr().String()
+func (t *YggdrasilTransport) streamAcceptLoop(yc *yggdrasilConnection) {
+	host := yc.RemoteAddr().String()
 
-	defer qc.CloseWithError(0, "Timed out") // nolint:errcheck
-	defer t.sessions.Delete(host)
+	defer yc.CloseWithError(0, "Timed out") // nolint:errcheck
+	defer t.connections.Delete(host)
 
 	for {
-		qs, err := qc.AcceptStream(context.Background())
+		qs, err := yc.AcceptStream(yc.Context)
 		if err != nil {
-			break
+			yc.CancelFunc()
+			return
+		}
+		select {
+		case t.incoming <- &yggdrasilStream{yc.Connection, qs}:
+		case <-yc.Context.Done():
+			return
 		}
-		t.incoming <- &yggdrasilSession{qc, qs}
 	}
 }
 
@@ -118,20 +142,32 @@ func (t *YggdrasilTransport) DialContext(ctx context.Context, network, host stri
 	}
 	ctx, cancel := context.WithTimeout(ctx, time.Second*5)
 	defer cancel()
-	var retry bool
+
+	// We might want to retrying once if part of the dial process fails,
+	// but keep a track of whether we're already retrying.
+	var retrying bool
 retry:
-	qc, ok := t.sessions.Load(host)
+	yc, ok := t.connections.Load(host)
 	if !ok {
+		// Check if there is already a dial to this host in progress.
+		// If there is then we will wait for it.
 		if dial, ok := t.dials.Load(host); ok {
 			<-dial.(*yggdrasilDial).Done()
 		}
-		if qc, ok = t.sessions.Load(host); !ok {
+
+		// Even after a dial, there's no connection. This means we
+		// probably failed to dial, so let's try it again.
+		if yc, ok = t.connections.Load(host); !ok {
+			// A cancellable context means we can cancel the dial in
+			// progress from elsewhere if we need to.
 			dialctx, dialcancel := context.WithCancel(ctx)
 			defer dialcancel()
 
+			// Make a record of the dial context.
 			t.dials.Store(host, &yggdrasilDial{dialctx, dialcancel})
 			defer t.dials.Delete(host)
 
+			// Decode the address from hex.
 			addr := make(iwt.Addr, ed25519.PublicKeySize)
 			k, err := hex.DecodeString(host)
 			if err != nil {
@@ -139,29 +175,40 @@ retry:
 			}
 			copy(addr, k)
 
+			// Attempt to open a QUIC session.
+			var qc quic.Connection
 			if qc, err = t.transport.Dial(dialctx, addr, t.tlsConfig, t.quicConfig); err != nil {
 				return nil, err
 			}
 
-			qc := qc.(quic.Connection)
-			t.sessions.Store(host, qc)
-			go t.streamAcceptLoop(qc)
+			// If we succeeded then we'll store our QUIC connection so
+			// that the next dial can open a stream on it directly. Start
+			// the accept loop so that streams can be accepted.
+			{
+				ctx, cancel := context.WithCancel(context.Background())
+				yc = &yggdrasilConnection{ctx, cancel, qc, make(chan struct{})}
+				t.connections.Store(host, yc)
+				go t.streamAcceptLoop(yc.(*yggdrasilConnection))
+			}
 		}
 	}
-	if qc == nil {
-		return nil, net.ErrClosed
-	} else {
-		qc := qc.(quic.Connection)
-		qs, err := qc.OpenStreamSync(ctx)
+	if yc, ok := yc.(*yggdrasilConnection); ok {
+		// We've either found a session or we successfully
+		// dialed a new one, so open a stream on it.
+		qs, err := yc.OpenStreamSync(ctx)
 		if err != nil {
-			if !retry {
-				retry = true
+			// We failed to open a stream, so if this isn't a
+			// retry, then let's try opening a new connection.
+			if !retrying {
+				retrying = true
 				goto retry
 			}
 			return nil, err
 		}
-		return &yggdrasilSession{qc, qs}, err
+		return &yggdrasilStream{yc.Connection, qs}, err
 	}
+	// We failed to open a session.
+	return nil, net.ErrClosed
 }
 
 func (t *YggdrasilTransport) Accept() (net.Conn, error) {
diff --git a/yggquic_test.go b/yggquic_test.go
index 7f2e5a3..e6c4c65 100644
--- a/yggquic_test.go
+++ b/yggquic_test.go
@@ -38,11 +38,11 @@ func TestQUICOverYggdrasil(t *testing.T) {
 	go node2.HandleConn(node1.PublicKey(), r, 0) // nolint:errcheck
 
 	// Create QUIC over Yggdrasil endpoints.
-	quic1, err := New(node1, *cfg1.Certificate)
+	quic1, err := New(node1, *cfg1.Certificate, nil)
 	if err != nil {
 		t.Fatal(err)
 	}
-	quic2, err := New(node2, *cfg2.Certificate)
+	quic2, err := New(node2, *cfg2.Certificate, nil)
 	if err != nil {
 		t.Fatal(err)
 	}