diff --git a/mitmproxy/proxy/layers/tls.py b/mitmproxy/proxy/layers/tls.py
index d8a33ac9c..cdc3bdec0 100644
--- a/mitmproxy/proxy/layers/tls.py
+++ b/mitmproxy/proxy/layers/tls.py
@@ -254,7 +254,11 @@ class _TLSLayer(tunnel.TunnelLayer):
             yield from super().receive_close()
 
     def send_data(self, data: bytes) -> layer.CommandGenerator[None]:
-        self.tls.sendall(data)
+        try:
+            self.tls.sendall(data)
+        except SSL.ZeroReturnError:
+            # The other peer may still be trying to send data over, which we discard here.
+            pass
         yield from self.tls_interact()
 
     def send_close(self, half_close: bool) -> layer.CommandGenerator[None]:
diff --git a/mitmproxy/proxy/tunnel.py b/mitmproxy/proxy/tunnel.py
index 14c54c6f5..bd622aeb9 100644
--- a/mitmproxy/proxy/tunnel.py
+++ b/mitmproxy/proxy/tunnel.py
@@ -75,7 +75,7 @@ class TunnelLayer(layer.Layer):
                 if self.tunnel_state is TunnelState.OPEN:
                     yield from self.receive_close()
                 elif self.tunnel_state is TunnelState.ESTABLISHING:
-                    err = "connection closed without notice"
+                    err = "connection closed"
                     yield from self.on_handshake_error(err)
                     yield from self._handshake_finished(err)
                 self.tunnel_state = TunnelState.CLOSED
diff --git a/test/mitmproxy/proxy/layers/test_tls.py b/test/mitmproxy/proxy/layers/test_tls.py
index f158bb53d..28b8625c6 100644
--- a/test/mitmproxy/proxy/layers/test_tls.py
+++ b/test/mitmproxy/proxy/layers/test_tls.py
@@ -509,6 +509,6 @@ class TestClientTLS:
                 << commands.SendData(tctx.client, tutils.Placeholder())
                 >> events.ConnectionClosed(tctx.client)
                 << commands.Log("Client TLS handshake failed. The client may not trust the proxy's certificate "
-                                "for wrong.host.mitmproxy.org (connection closed without notice)", "warn")
+                                "for wrong.host.mitmproxy.org (connection closed)", "warn")
                 << commands.CloseConnection(tctx.client)
         )
diff --git a/test/mitmproxy/proxy/test_tunnel.py b/test/mitmproxy/proxy/test_tunnel.py
index 6f852ce68..68baad6db 100644
--- a/test/mitmproxy/proxy/test_tunnel.py
+++ b/test/mitmproxy/proxy/test_tunnel.py
@@ -245,7 +245,7 @@ def test_disconnect_during_handshake_command(tctx: Context, disconnect):
                 >> ConnectionClosed(tctx.client)
                 >> ConnectionClosed(server)  # proxyserver will cancel all other connections as well.
                 << CloseConnection(server)
-                << Log("Opened: err='connection closed without notice'. Server state: CLOSED")
+                << Log("Opened: err='connection closed'. Server state: CLOSED")
                 << Log("Got client close.")
                 << CloseConnection(tctx.client)
         )
@@ -254,7 +254,7 @@ def test_disconnect_during_handshake_command(tctx: Context, disconnect):
                 playbook
                 >> ConnectionClosed(server)
                 << CloseConnection(server)
-                << Log("Opened: err='connection closed without notice'. Server state: CLOSED")
+                << Log("Opened: err='connection closed'. Server state: CLOSED")
         )