diff --git a/app/models/message/broadcasts.rb b/app/models/message/broadcasts.rb
index b9660c9..6ae7569 100644
--- a/app/models/message/broadcasts.rb
+++ b/app/models/message/broadcasts.rb
@@ -9,11 +9,13 @@ module Message::Broadcasts
   end
 
   # Fanned out to the room's members rather than published on one global stream, so
-  # that the timing of activity in a room only reaches people who are in it.
+  # that the timing of activity in a room only reaches people who are in it. Of those,
+  # only the ones who still have it unread or are in it now: by the time this runs,
+  # someone may have opened the room and moved on, and would see it marked unread again.
   def broadcast_unread_room
     payload = ActiveSupport::JSON.encode(roomId: room.id)
 
-    room.memberships.pluck(:user_id).each do |user_id|
+    room.memberships.unread.or(room.memberships.connected).pluck(:user_id).each do |user_id|
       ActionCable.server.broadcast UnreadRoomsChannel.stream_name_for(user_id), payload, coder: nil
     end
   end
diff --git a/test/controllers/messages_controller_test.rb b/test/controllers/messages_controller_test.rb
index 63266cb..83cedda 100644
--- a/test/controllers/messages_controller_test.rb
+++ b/test/controllers/messages_controller_test.rb
@@ -58,6 +58,8 @@ class MessagesControllerTest < ActionDispatch::IntegrationTest
   end
 
   test "creating a message broadcasts unread room to each member" do
+    memberships(:david_watercooler).present # the poster is in the room
+
     @room.users.each do |member|
       assert_broadcasts UnreadRoomsChannel.stream_name_for(member.id), 1 do
         perform_enqueued_jobs only: Message::BroadcastUnreadRoomJob do
@@ -77,6 +79,20 @@ class MessagesControllerTest < ActionDispatch::IntegrationTest
     assert_enqueued_with job: Message::BroadcastUnreadRoomJob, args: [ Message.last ]
   end
 
+  test "the unread fanout skips a member who has opened the room since" do
+    membership = memberships(:jason_watercooler)
+
+    post room_messages_url(@room, format: :turbo_stream), params: { message: { body: "New one", client_message_id: 999 } }
+    assert membership.reload.unread?
+
+    membership.present
+    membership.reload.disconnected
+
+    assert_no_broadcasts UnreadRoomsChannel.stream_name_for(membership.user_id) do
+      perform_enqueued_jobs only: Message::BroadcastUnreadRoomJob
+    end
+  end
+
   test "creating a message doesn't broadcast unread room to non-members" do
     outsiders = User.where.not(id: @room.users.map(&:id))
     assert outsiders.any?, "need someone outside the room for this test to mean anything"