diff --git a/conn.go b/conn.go
index e867aec..a7b04c3 100644
--- a/conn.go
+++ b/conn.go
@@ -456,6 +456,10 @@ func (conn *Conn) handlePacket(b []byte) error {
 	if len(b) == 0 {
 		return errZeroPacket
 	}
+	if conn.closing.Load() != 0 {
+		// Don't continue handling packets if the connection is being closed.
+		return nil
+	}
 	handled, err := conn.handler.handle(conn, b)
 	if err != nil {
 		return fmt.Errorf("handle packet: %w", err)
@@ -623,7 +627,7 @@ func (conn *Conn) writeTo(p []byte, raddr net.Addr) error {
 	if _, err := conn.conn.WriteTo(p, raddr); errors.Is(err, net.ErrClosed) {
 		return fmt.Errorf("write to: %w", err)
 	} else if err != nil {
-		conn.handler.log().Error("write to: " + err.Error())
+		conn.handler.log().Error("write to: "+err.Error(), "raddr", raddr.String())
 	}
 	return nil
 }
diff --git a/dial.go b/dial.go
index 6e16d42..f019e06 100644
--- a/dial.go
+++ b/dial.go
@@ -218,6 +218,7 @@ func (dialer Dialer) DialContext(ctx context.Context, address string) (*Conn, er
 	if err != nil {
 		return nil, dialer.error("dial", err)
 	}
+	dialer.ErrorLog = dialer.ErrorLog.With("src", "dialer", "raddr", conn.RemoteAddr().String())
 
 	cs := &connState{conn: conn, raddr: conn.RemoteAddr(), id: atomic.AddInt64(&dialerID, 1), ticker: time.NewTicker(time.Second / 2)}
 	defer cs.ticker.Stop()
@@ -268,7 +269,7 @@ func (dialer Dialer) clientListen(rakConn *Conn, conn net.Conn) {
 			}
 			// Errors reading a packet other than the connection being
 			// closed may be worth logging.
-			dialer.ErrorLog.Error("client: " + err.Error())
+			dialer.ErrorLog.Error("handle packet: " + err.Error())
 		}
 	}
 }
diff --git a/handler.go b/handler.go
index 261d20c..735f1a3 100644
--- a/handler.go
+++ b/handler.go
@@ -70,9 +70,10 @@ func (h listenerConnectionHandler) handleUnconnected(b []byte, addr net.Addr) er
 		// In some cases, the client will keep trying to send datagrams
 		// while it has already timed out. In this case, we should not return
 		// an error.
+		h.log().Debug("unexpected datagram", "raddr", addr.String())
 		return nil
 	}
-	return fmt.Errorf("unknown packet received (id=%x, len=%v)", b[0], len(b))
+	return fmt.Errorf("unknown unconnected packet (id=%x, len=%v)", b[0], len(b))
 }
 
 // handleUnconnectedPing handles an unconnected ping packet stored in buffer b,
diff --git a/listener.go b/listener.go
index 6b743ad..d081174 100644
--- a/listener.go
+++ b/listener.go
@@ -83,6 +83,8 @@ func (conf ListenConfig) Listen(address string) (*Listener, error) {
 	if conf.ErrorLog == nil {
 		conf.ErrorLog = slog.New(internal.DiscardHandler{})
 	}
+	conf.ErrorLog = conf.ErrorLog.With("src", "listener")
+
 	if conf.BlockDuration == 0 {
 		conf.BlockDuration = time.Second * 10
 	}
@@ -184,7 +186,7 @@ func (listener *Listener) listen() {
 			continue
 		}
 		if err = listener.handle(b[:n], addr); err != nil && !errors.Is(err, net.ErrClosed) {
-			listener.conf.ErrorLog.Error("listener: handle packet: "+err.Error(), "address", addr.String(), "block-duration", max(0, listener.conf.BlockDuration))
+			listener.conf.ErrorLog.Error("handle packet: "+err.Error(), "raddr", addr.String(), "block-duration", max(0, listener.conf.BlockDuration))
 			listener.sec.block(addr)
 		}
 	}