diff --git a/game/scripts/net_link.gd b/game/scripts/net_link.gd
index 1e5ed2c..65aad40 100644
--- a/game/scripts/net_link.gd
+++ b/game/scripts/net_link.gd
@@ -20,6 +20,9 @@ var connect_seconds := CONNECT_SECONDS
 
 var _peer: ENetMultiplayerPeer
 var _peers: Dictionary[int, bool] = {}
+## Connections that close_peer is closing. Nothing more goes to them: Godot
+## reports an error for every packet to a connection in that state.
+var _closing: Dictionary[int, bool] = {}
 var _events: Array[Dictionary] = []
 var _connecting := false
 var _waited := 0.0
@@ -67,6 +70,7 @@ func _start() -> void:
 	close()
 	_peer = ENetMultiplayerPeer.new()
 	_peers.clear()
+	_closing.clear()
 	_peer.peer_connected.connect(_on_connected)
 	_peer.peer_disconnected.connect(_on_disconnected)
 
@@ -78,6 +82,7 @@ func _on_connected(peer: int) -> void:
 
 func _on_disconnected(peer: int) -> void:
 	_peers.erase(peer)
+	_closing.erase(peer)
 	_events.append({"type": "disconnected", "peer": peer})
 
 
@@ -118,7 +123,7 @@ func poll(delta: float) -> Array[Dictionary]:
 
 
 ## Sends a message of the core to `peer`, reliably and in order. A message
-## to a connection that is gone is dropped.
+## to a connection that is gone or being closed is dropped.
 func send(peer: int, bytes: PackedByteArray) -> void:
 	_put(peer, bytes, CHANNEL_CORE, MultiplayerPeer.TRANSFER_MODE_RELIABLE)
 
@@ -130,19 +135,34 @@ func send_figure(peer: int, bytes: PackedByteArray) -> void:
 
 
 func _put(peer: int, bytes: PackedByteArray, channel: int, mode: MultiplayerPeer.TransferMode) -> void:
-	if not is_connected_to_peers() or _peers.is_empty():
+	if not is_connected_to_peers():
 		return
-	if peer > 0 and not _peers.has(peer):
-		return
-	_peer.set_target_peer(peer)
 	_peer.set_transfer_channel(channel)
 	_peer.set_transfer_mode(mode)
-	_peer.put_packet(bytes)
+	# One packet per connection, so that no packet goes to a connection that
+	# is gone or being closed; Godot's own sending to all would.
+	for target in _targets(peer):
+		_peer.set_target_peer(target)
+		_peer.put_packet(bytes)
+
+
+## The connections a packet for `peer` goes to: that one, every one if
+## `peer` is 0, or every one but -`peer` if `peer` is negative. Connections
+## that are being closed get nothing.
+func _targets(peer: int) -> Array[int]:
+	var targets: Array[int] = []
+	for open: int in _peers:
+		if _closing.has(open):
+			continue
+		if peer == 0 or open == peer or (peer < 0 and open != -peer):
+			targets.append(open)
+	return targets
 
 
 ## Closes the connection to `peer` once the messages waiting for it are out.
 func close_peer(peer: int) -> void:
-	if _peers.has(peer):
+	if _peers.has(peer) and not _closing.has(peer):
+		_closing[peer] = true
 		_peer.get_peer(peer).peer_disconnect_later()
 
 
@@ -151,4 +171,5 @@ func close() -> void:
 	if is_open():
 		_peer.close()
 	_peers.clear()
+	_closing.clear()
 	_connecting = false
diff --git a/game/tests/test_net_link.gd b/game/tests/test_net_link.gd
index 4cf5a85..68daffa 100644
--- a/game/tests/test_net_link.gd
+++ b/game/tests/test_net_link.gd
@@ -100,14 +100,43 @@ func test_a_guest_that_quits_is_seen_leaving() -> void:
 	host.close()
 
 
-func test_messages_to_a_connection_that_is_gone_are_dropped() -> void:
+## Godot reports an error for every packet to a connection that is gone or
+## being closed; the test runner turns each such error into a failure.
+func test_nothing_is_sent_to_connections_that_are_gone_or_closing() -> void:
 	var host := NetLink.new()
 	check_eq(host.host(0, "127.0.0.1"), OK, "the host listens")
+	var first := NetLink.new()
+	var second := NetLink.new()
+	first.join("127.0.0.1", host.local_port())
+	second.join("127.0.0.1", host.local_port())
+	await _pump([host, first, second], 10)
+	var peers: Array = _events[host].map(func(event: Dictionary) -> int: return event["peer"])
+	check_eq(peers.size(), 2, "two guests connected")
+	var leaving: int = peers[0]
+	var staying: int = peers[1]
+
+	# Connections that never existed.
 	host.send(12345, PackedByteArray([1]))
 	host.send_figure(12345, PackedByteArray([1]))
+	host.send_figure(-12345, PackedByteArray([1]))
 	host.close_peer(12345)
-	check_eq(host.poll(0.0), [], "nothing happened")
-	host.close()
+	# A connection that is being closed, and everybody while it closes.
+	host.close_peer(leaving)
+	for frame in 10:
+		host.send(leaving, PackedByteArray([2]))
+		host.send_figure(leaving, PackedByteArray([2]))
+		host.send_figure(-staying, PackedByteArray([2]))
+		host.send_figure(0, PackedByteArray([2]))
+		await _pump([host, first, second], 1)
+	# The connection is gone now.
+	host.send(leaving, PackedByteArray([3]))
+	host.send_figure(-leaving, PackedByteArray([3]))
+	await _pump([host, first, second], 5)
+
+	check(_types(first).has("disconnected"), "the first guest was closed")
+	check(not _types(second).has("disconnected"), "the second guest stays")
+	for link in [host, first, second]:
+		link.close()
 
 
 func test_a_guest_gives_up_when_nobody_answers() -> void: