diff --git a/agent_docs/map-travel.md b/agent_docs/map-travel.md
index 90444822c..6dab0fe17 100644
--- a/agent_docs/map-travel.md
+++ b/agent_docs/map-travel.md
@@ -214,16 +214,19 @@ it for the player, who goes in with the portal sound. The party members
 who were beside the leader follow to the copy's `out00` once the leader is
 in (`ServerMessage::ShipWarp`). A copy's `out00`, like `MD00` anywhere but the base map,
 leads back to the base map's `MD00`. When the player who took the copy
-leaves it (by map change, logout, logging in again or channel change),
-everyone still in it is sent to the base map's portal 0. An empty copy puts its mobs back, as a
+leaves it (by map change, logout or logging in again),
+everyone still in it is sent to the base map's portal 0. If the leader
+hands the party to a member in the copy, the copy goes with it; if the new
+leader is anywhere else, the run ends the same way, as in Cosmic
+(`WorldDirectory::dungeon_leader_changed`). Nobody in a copy may change channel or
+enter the Cash Shop: both get the client's own refusal (BLOCKED_SERVER 1
+and 2). An empty copy puts its mobs back, as a
 clone's room does (`npc_scripts::resets_when_empty`). The clock is each
-player's own `MapTimer`, and a login or channel change into a copy lands
+player's own `MapTimer`, and a login into a copy lands
 on its forced return map.
 
-Not yet: the Cash Shop isn't closed to players in a copy, a party's new
-leader doesn't close the run (Cosmic closes it when the leadership passes
-to someone on another map), and the time limit runs per player rather than
-per copy.
+Not yet: the time limit runs per player rather than per copy (the members
+follow the leader in within seconds, so the clocks hardly differ).
 
 Only the `go<map id>` banners are used by the current maps, on the Adventurer
 Training Centers and the revamp's Southperry (`2000000`). The other scripts,
diff --git a/net/src/packet/handle/world/cash_shop.rs b/net/src/packet/handle/world/cash_shop.rs
index 4ffff44f5..10b0c7f62 100644
--- a/net/src/packet/handle/world/cash_shop.rs
+++ b/net/src/packet/handle/world/cash_shop.rs
@@ -14,7 +14,9 @@ pub struct EnterCashShopHandler;
 
 impl WorldHandler for EnterCashShopHandler {
     fn handle(&self, _packet: &mut Packet, ctx: &mut WorldContext) -> WorldResult {
-        if ctx.player.stats.hp <= 0 {
+        // Nor does anyone leave a mini-dungeon's copy for the shop (as in
+        // Cosmic): the copy would be free for others while they are away.
+        if ctx.player.stats.hp <= 0 || crate::dungeons::of_copy(ctx.player.stats.map_id).is_some() {
             return Ok(HandlerResult::reply(
                 build::world::map::build_blocked_server(BlockedServer::CashShop)?,
             ));
@@ -234,6 +236,26 @@ mod tests {
         ));
     }
 
+    #[test]
+    fn nobody_leaves_a_mini_dungeon_for_the_cash_shop() {
+        let mut player = crate::codec::stats::sample_player();
+        player.stats.map_id = 100020100;
+        let mut ctx = WorldContext {
+            client_id: 1,
+            channel_id: 0,
+            player: &mut player,
+        };
+        let mut packet = Packet::new_empty();
+        packet
+            .write_short(RecvOpcode::EnterCashShop as i16)
+            .unwrap();
+        let result = EnterCashShopHandler.handle(&mut packet, &mut ctx).unwrap();
+        assert!(matches!(
+            result.actions.as_slice(),
+            [WorldAction::Reply(p)] if p.bytes == [0x84, 0, 2]
+        ));
+    }
+
     #[test]
     fn an_unknown_balance_fails_the_purchase() {
         let result = handle(|p| {
diff --git a/net/src/packet/handle/world/change_channel.rs b/net/src/packet/handle/world/change_channel.rs
index 361a5e24d..5edcf8bf2 100644
--- a/net/src/packet/handle/world/change_channel.rs
+++ b/net/src/packet/handle/world/change_channel.rs
@@ -15,9 +15,11 @@ impl WorldHandler for ChangeChannelHandler {
         let _tick = reader.read_int()?;
 
         // The client waits on an answer before it sends another request, so
-        // a refusal still answers.
+        // a refusal still answers. A mini-dungeon's copy is kept on its
+        // channel, so nobody leaves it that way (as in Cosmic).
         if target_channel_id == ctx.channel_id
             || resolve_login_channel(ctx.player.world_id, target_channel_id).is_err()
+            || crate::dungeons::of_copy(ctx.player.stats.map_id).is_some()
         {
             return Ok(HandlerResult::reply(
                 build::world::map::build_blocked_server(BlockedServer::Channel)?,
@@ -29,3 +31,32 @@ impl WorldHandler for ChangeChannelHandler {
         }))
     }
 }
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::packet::op::RecvOpcode;
+    use packet::io::write::PktWrite;
+
+    #[test]
+    fn nobody_changes_channel_inside_a_mini_dungeon() {
+        let mut player = crate::codec::stats::sample_player();
+        player.stats.map_id = 100020100;
+        let mut ctx = WorldContext {
+            client_id: 1,
+            channel_id: 0,
+            player: &mut player,
+        };
+        let mut packet = Packet::new_empty();
+        packet
+            .write_short(RecvOpcode::ChangeChannel as i16)
+            .unwrap();
+        packet.write_byte(1).unwrap();
+        packet.write_int(0).unwrap();
+        let result = ChangeChannelHandler.handle(&mut packet, &mut ctx).unwrap();
+        assert!(matches!(
+            result.actions.as_slice(),
+            [WorldAction::Reply(p)] if p.bytes == [0x84, 0, 1]
+        ));
+    }
+}
diff --git a/runtime/src/actor/directory.rs b/runtime/src/actor/directory.rs
index 4d8973666..86ff85e6c 100644
--- a/runtime/src/actor/directory.rs
+++ b/runtime/src/actor/directory.rs
@@ -539,6 +539,43 @@ impl WorldDirectory {
         }
     }
 
+    /// `from` handed their party to `to`. A mini-dungeon's copy `from` took
+    /// goes with it if `to` is in it too; if not, the run is over and
+    /// everyone in it goes back to the dungeon's map (as in Cosmic).
+    fn dungeon_leader_changed(&mut self, from: ClientId, to: ClientId) {
+        let Some(entry) = self.clients.get(&from) else {
+            return;
+        };
+        let (channel_id, map_id) = (entry.channel_id, entry.presence.map_id);
+        let Some(run) = self
+            .dungeons
+            .get_mut(&(channel_id, map_id))
+            .filter(|run| run.leader == from)
+        else {
+            return;
+        };
+        let beside = self
+            .clients
+            .get(&to)
+            .is_some_and(|other| other.channel_id == channel_id && other.presence.map_id == map_id);
+        if beside {
+            run.leader = to;
+            return;
+        }
+        if let Some(dungeon) = net::dungeons::of_copy(map_id) {
+            for entry in self.clients.values() {
+                if entry.channel_id == channel_id && entry.presence.map_id == map_id {
+                    entry.handle.send(ServerMessage::ShipWarp {
+                        from_map: map_id,
+                        map_id: dungeon.base,
+                        portal: Portal::Id(0),
+                    });
+                }
+            }
+        }
+        self.dungeons.remove(&(channel_id, map_id));
+    }
+
     /// `client_id` left `map_id` on `channel_id`. If it is a mini-dungeon's
     /// copy they took, the run is over: whoever is still in it goes back to
     /// the dungeon's map.
@@ -1208,6 +1245,7 @@ impl WorldDirectory {
                 }
                 if let Some(party) = self.parties.change_leader(from, member_id).cloned() {
                     self.send_to_party(&party, |_| build_party_leader_changed(member_id));
+                    self.dungeon_leader_changed(from, member_id);
                 }
             }
             PartyRequest::Chat { text } => {
@@ -2411,6 +2449,44 @@ mod tests {
         assert_eq!(ship_warps(&mut bobby), [(FIRST, PIG_FARM)]);
     }
 
+    #[test]
+    fn a_mini_dungeon_follows_a_new_leader_in_it_and_closes_for_one_outside() {
+        const PIG_FARM: i32 = 100020000;
+        const FIRST: i32 = 100020100;
+        let (_tx, rx) = mpsc::channel(1);
+        let mut directory = WorldDirectory::new(rx);
+        let mut alice = online(&mut directory, 1, "Alice", PIG_FARM);
+        let mut bobby = online(&mut directory, 2, "Bobby", PIG_FARM);
+        let _carol = online(&mut directory, 3, "Carol", 20000);
+        let now = Instant::now();
+        for name in ["Bobby", "Carol"] {
+            let name = name.into();
+            directory.party_request(1, PartyRequest::Invite { name }, now);
+        }
+        for id in [2, 3] {
+            directory.party_request(id, PartyRequest::Accept { party_id: 1 }, now);
+        }
+        assert_eq!(directory.enter_dungeon(1, FIRST, 1, now), Ok(FIRST));
+        directory.gather_team(1, FIRST, 0);
+        directory.update_presence(1, presence("Alice", FIRST));
+        directory.update_presence(2, presence("Bobby", FIRST));
+        ship_warps(&mut bobby);
+
+        // Bobby, in the copy with her, takes it over: Alice may leave.
+        directory.party_request(1, PartyRequest::ChangeLeader { member_id: 2 }, now);
+        directory.update_presence(1, presence("Alice", PIG_FARM));
+        assert_eq!(ship_warps(&mut bobby), []);
+        assert!(directory.dungeons.contains_key(&(0, FIRST)));
+
+        // Carol is elsewhere, so handing her the party ends the run.
+        directory.update_presence(1, presence("Alice", FIRST));
+        ship_warps(&mut alice);
+        directory.party_request(2, PartyRequest::ChangeLeader { member_id: 3 }, now);
+        assert_eq!(ship_warps(&mut alice), [(FIRST, PIG_FARM)]);
+        assert_eq!(ship_warps(&mut bobby), [(FIRST, PIG_FARM)]);
+        assert!(!directory.dungeons.contains_key(&(0, FIRST)));
+    }
+
     #[test]
     fn duplicate_login_kicks_the_previous_connection_only() {
         let (_tx, rx) = mpsc::channel(1);