diff --git a/conn.go b/conn.go
index 82ee4eb..576d308 100644
--- a/conn.go
+++ b/conn.go
@@ -172,6 +172,7 @@ type conn struct {
 	lock     sync.Mutex
 	outgoing chan<- *irc.Message
 	closed   bool
+	closedCh chan struct{}
 }
 
 func newConn(srv *Server, ic ircConn, options *connOptions) *conn {
@@ -181,6 +182,7 @@ func newConn(srv *Server, ic ircConn, options *connOptions) *conn {
 		srv:      srv,
 		outgoing: outgoing,
 		logger:   options.Logger,
+		closedCh: make(chan struct{}),
 	}
 
 	go func() {
@@ -237,6 +239,7 @@ func (c *conn) Close() error {
 	err := c.conn.Close()
 	c.closed = true
 	close(c.outgoing)
+	close(c.closedCh)
 	return err
 }
 
@@ -277,3 +280,28 @@ func (c *conn) RemoteAddr() net.Addr {
 func (c *conn) LocalAddr() net.Addr {
 	return c.conn.LocalAddr()
 }
+
+// NewContext returns a copy of the parent context with a new Done channel. The
+// returned context's Done channel is closed when the connection is closed,
+// when the returned cancel function is called, or when the parent context's
+// Done channel is closed, whichever happens first.
+//
+// Canceling this context releases resources associated with it, so code should
+// call cancel as soon as the operations running in this Context complete.
+func (c *conn) NewContext(parent context.Context) (context.Context, context.CancelFunc) {
+	ctx, cancel := context.WithCancel(parent)
+
+	go func() {
+		defer cancel()
+
+		select {
+		case <-ctx.Done():
+			// The parent context has been cancelled, or the caller has called
+			// cancel()
+		case <-c.closedCh:
+			// The connection has been closed
+		}
+	}()
+
+	return ctx, cancel
+}
diff --git a/downstream.go b/downstream.go
index eb31a61..cce1305 100644
--- a/downstream.go
+++ b/downstream.go
@@ -615,7 +615,10 @@ func (dc *downstreamConn) marshalMessage(msg *irc.Message, net *network) *irc.Me
 }
 
 func (dc *downstreamConn) handleMessage(msg *irc.Message) error {
-	ctx, cancel := context.WithTimeout(context.TODO(), handleDownstreamMessageTimeout)
+	ctx, cancel := dc.conn.NewContext(context.TODO())
+	defer cancel()
+
+	ctx, cancel = context.WithTimeout(ctx, handleDownstreamMessageTimeout)
 	defer cancel()
 
 	switch msg.Command {