diff --git a/src/dwarves.rs b/src/dwarves.rs
index 5c02942..3ad8c5a 100644
--- a/src/dwarves.rs
+++ b/src/dwarves.rs
@@ -195,7 +195,7 @@ impl Game {
             e.repath = 3.0 + self.rng.f() * 4.0;
             let (tx, ty) = if from_home(e.x, e.y) > 3.0 { (hx, hy) } else { (hx + self.rng.f() * 4.0 - 2.0, hy + self.rng.f() * 4.0 - 2.0) };
             if self.map.walk(tx as i32, ty as i32) {
-                if let Some(p) = self.map.path_to(e.tile(), idx(tx as i32, ty as i32)) {
+                if let Some(p) = self.map.creature_path(flies(e.kind), e.tile(), idx(tx as i32, ty as i32)) {
                     e.path = p;
                 }
             }
diff --git a/src/game.rs b/src/game.rs
index 175e507..32393a3 100644
--- a/src/game.rs
+++ b/src/game.rs
@@ -1692,7 +1692,7 @@ impl Game {
         }
         let cur = e.tile();
         let near = |i: usize| tasks.iter().copied().find(|&t| i != t && adj4(i, t) || (i == t && self.map.t[t].walkable()));
-        let Some(p) = self.map.search(cur, self.map.walk_cost(), |i| near(i).is_some(), true) else { return false };
+        let Some(p) = self.map.search(cur, self.map.creature_cost(flies(e.kind)), |i| near(i).is_some(), true) else { return false };
         let end = p.last().copied().unwrap_or(cur);
         let Some(t) = near(end) else { return false };
         e.path = p;
@@ -3387,10 +3387,10 @@ impl Game {
 
     // ---------------------------------------------------------------- creatures
 
-    fn find_room_tile(&self, cur: usize, kind: Kind, me: u32, need_food: bool) -> Option<Vec<usize>> {
+    fn find_room_tile(&self, e: &Ent, kind: Kind, me: u32, need_food: bool) -> Option<Vec<usize>> {
         self.map.search(
-            cur,
-            self.map.walk_cost(),
+            e.tile(),
+            self.map.creature_cost(flies(e.kind)),
             |i| {
                 let t = &self.map.t[i];
                 t.kind == kind && t.owner == self.me && (t.reserved == 0 || t.reserved == me) && (!need_food || t.food >= 1.0)
@@ -3905,7 +3905,7 @@ impl Game {
             return;
         }
         if e.hunger > 1.0 && !(self.flag.is_some() && e.hunger < 1.5) {
-            if let Some(p) = self.find_room_tile(cur, Kind::Farm, me, true) {
+            if let Some(p) = self.find_room_tile(e, Kind::Farm, me, true) {
                 let t = p.last().copied().unwrap_or(cur);
                 self.map.t[t].reserved = me;
                 e.path = p;
@@ -3939,7 +3939,7 @@ impl Game {
         if self.counts[6] > 0 {
             let r2 = self.rng.f();
             if r2 < 0.3 || (e.kind == EK::Priestess && r2 < 0.7) {
-                if let Some(p) = self.find_room_tile(cur, Kind::Temple, me, false) {
+                if let Some(p) = self.find_room_tile(e, Kind::Temple, me, false) {
                     let t = p.last().copied().unwrap_or(cur);
                     self.map.t[t].reserved = me;
                     e.path = p;
@@ -3974,7 +3974,7 @@ impl Game {
             }
         }
         if self.counts[crate::rooms::ROOM_ARENA] > 0 && e.hp > e.max_hp * 0.8 && self.rng.f() < 0.25 {
-            if let Some(p) = self.find_room_tile(cur, Kind::Arena, me, false) {
+            if let Some(p) = self.find_room_tile(e, Kind::Arena, me, false) {
                 let t = p.last().copied().unwrap_or(cur);
                 self.map.t[t].reserved = me;
                 e.path = p;
@@ -3987,7 +3987,7 @@ impl Game {
         if self.forge_orders() && self.counts[ROOM_FORGE] > 0 {
             let r = self.rng.f();
             if (e.kind == EK::Cogling && r < 0.9) || r < 0.25 {
-                if let Some(p) = self.find_room_tile(cur, Kind::Forge, me, false) {
+                if let Some(p) = self.find_room_tile(e, Kind::Forge, me, false) {
                     let t = p.last().copied().unwrap_or(cur);
                     self.map.t[t].reserved = me;
                     e.path = p;
@@ -3999,7 +3999,7 @@ impl Game {
         }
         let r = self.rng.f();
         if (e.kind == EK::Mage && r < 0.8) || r < 0.2 {
-            if let Some(p) = self.find_room_tile(cur, Kind::Library, me, false) {
+            if let Some(p) = self.find_room_tile(e, Kind::Library, me, false) {
                 let t = p.last().copied().unwrap_or(cur);
                 self.map.t[t].reserved = me;
                 e.path = p;
@@ -4009,7 +4009,7 @@ impl Game {
             }
         }
         if r < 0.8 && self.gold >= 5.0 {
-            if let Some(p) = self.find_room_tile(cur, Kind::Training, me, false) {
+            if let Some(p) = self.find_room_tile(e, Kind::Training, me, false) {
                 let t = p.last().copied().unwrap_or(cur);
                 self.map.t[t].reserved = me;
                 e.path = p;
@@ -5935,6 +5935,43 @@ mod tests {
         assert!(best <= 2.0);
     }
 
+    #[test]
+    fn flyers_take_every_way_across_rivers() {
+        let (mut g, rx) = river_game(false);
+        let (cx, cy) = g.map.core;
+        // open floor on the far bank with one training tile of the player
+        for y in cy - 2..=cy + 2 {
+            for x in rx + 3..rx + 7 {
+                let t = &mut g.map.t[idx(x, y)];
+                t.kind = Kind::Floor;
+                t.owner = Owner::None;
+            }
+        }
+        let room = idx(rx + 4, cy);
+        g.map.t[room].kind = Kind::Training;
+        g.map.t[room].owner = g.me;
+        let owl = g.spawn(EK::Owl, false, (cx + 4) as f32 + 0.5, cy as f32 + 0.5, 1);
+        let kobold = g.spawn(EK::Kobold, false, (cx + 4) as f32 + 0.5, cy as f32 + 0.5, 1);
+        let owl = g.ents.iter().find(|e| e.id == owl).unwrap().clone();
+        let kobold = g.ents.iter().find(|e| e.id == kobold).unwrap().clone();
+        // room searches: the owl flies over the river to the training room, the kobold cannot get there
+        let p = g.find_room_tile(&owl, Kind::Training, owl.id + 1, false).expect("the owl finds the room across the river");
+        assert_eq!(p.last().copied(), Some(room));
+        assert!(g.find_room_tile(&kobold, Kind::Training, kobold.id + 1, false).map_or(true, |p| p.last() != Some(&room)));
+        // flyers cut corners over water: a diagonal crossing is as short as on open ground
+        let (a, b) = (idx(rx - 1, cy - 1), idx(rx + 3, cy + 1));
+        let p = g.map.creature_path(true, a, b).expect("flight path");
+        assert!(p.len() <= 5, "diagonal flight over the river: {} steps", p.len());
+        assert!(p.iter().any(|&i| g.map.t[i].liquid()));
+        // attacking flyers (the fairy spy) also fly over rivers instead of searching for a bridge
+        assert!(g.map.hero_cost_as(true)(idx(rx + 1, cy)).is_some());
+        assert_eq!(g.map.hero_cost()(idx(rx + 1, cy)), None);
+        // a locked door stops flyers too
+        g.map.t[idx(rx + 5, cy)].kind = Kind::Door;
+        g.map.t[idx(rx + 5, cy)].res = 1;
+        assert_eq!(g.map.fly_cost()(idx(rx + 5, cy)), None);
+    }
+
     #[test]
     fn flyers_cross_rivers_flee_and_heal() {
         let (mut g, rx) = river_game(true);
diff --git a/src/map.rs b/src/map.rs
index 62b6566..a4bed9a 100644
--- a/src/map.rs
+++ b/src/map.rs
@@ -656,7 +656,9 @@ impl Map {
                 let mut step = c * 10;
                 if k >= 4 {
                     // diagonal only if both neighbours are walkable (no corner cutting)
-                    if c > 1 || !self.walk(x + dx, y) || !self.walk(x, y + dy) {
+                    // (judged with the same cost, so flyers may cut corners over water and lava)
+                    let open = |cx: i32, cy: i32| cost(idx(cx, cy)) == Some(1);
+                    if c > 1 || !open(x + dx, y) || !open(x, y + dy) {
                         continue;
                     }
                     step = 14;
@@ -673,9 +675,22 @@ impl Map {
     }
 
     pub fn walk_cost(&self) -> impl Fn(usize) -> Option<u32> + '_ {
+        self.creature_cost(false)
+    }
+
+    // flying creatures also cross water and lava
+    pub fn fly_cost(&self) -> impl Fn(usize) -> Option<u32> + '_ {
+        self.creature_cost(true)
+    }
+
+    // the dungeon's creatures walk on open ground; flyers also cross water and lava
+    pub fn creature_cost(&self, fly: bool) -> impl Fn(usize) -> Option<u32> + '_ {
         move |i| {
             let t = &self.t[i];
-            // a locked door stops the dungeon's own creatures too
+            if fly && t.liquid() {
+                return Some(1);
+            }
+            // a locked door stops the dungeon's own creatures too (flyers included)
             if t.walkable() && !(t.kind == Kind::Door && t.res & 1 == 1) {
                 Some(1)
             } else {
@@ -684,9 +699,9 @@ impl Map {
         }
     }
 
-    // flying creatures also cross water and lava
-    pub fn fly_cost(&self) -> impl Fn(usize) -> Option<u32> + '_ {
-        move |i| if self.t[i].walkable() || self.t[i].liquid() { Some(1) } else { None }
+    // path for a walking or flying creature
+    pub fn creature_path(&self, fly: bool, start: usize, target: usize) -> Option<Vec<usize>> {
+        self.search(start, self.creature_cost(fly), |i| i == target, true)
     }
 
     pub fn fly_path_to(&self, start: usize, target: usize) -> Option<Vec<usize>> {
@@ -694,9 +709,15 @@ impl Map {
     }
 
     pub fn hero_cost(&self) -> impl Fn(usize) -> Option<u32> + '_ {
+        self.hero_cost_as(false)
+    }
+
+    // attackers dig through earth; flying ones also cross water and lava
+    pub fn hero_cost_as(&self, fly: bool) -> impl Fn(usize) -> Option<u32> + '_ {
         move |i| {
             let tl = &self.t[i];
             match tl.kind {
+                Kind::Water | Kind::Lava if fly => Some(1),
                 Kind::Earth if tl.reinforced => Some(70),
                 Kind::Steel => Some(300),
                 Kind::Earth => Some(7),
@@ -720,7 +741,11 @@ impl Map {
     }
 
     pub fn hero_path_to_core(&self, start: usize) -> Option<Vec<usize>> {
-        self.search(start, self.hero_cost(), |i| self.adj_core(i), true)
+        self.hero_path_to_core_as(false, start)
+    }
+
+    pub fn hero_path_to_core_as(&self, fly: bool, start: usize) -> Option<Vec<usize>> {
+        self.search(start, self.hero_cost_as(fly), |i| self.adj_core(i), true)
     }
 
 
diff --git a/src/orders.rs b/src/orders.rs
index 5924742..23d6ccd 100644
--- a/src/orders.rs
+++ b/src/orders.rs
@@ -97,7 +97,7 @@ impl Game {
         let mut n = 0;
         for (&j, &spot) in cands.iter().zip(spots.iter()).take(GUARDS) {
             let cur = self.ents[j].tile();
-            let Some(p) = self.map.path_to(cur, spot) else { continue };
+            let Some(p) = self.map.creature_path(flies(self.ents[j].kind), cur, spot) else { continue };
             let me = self.ents[j].id + 1;
             self.unreserve(me);
             self.map.t[spot].reserved = me;
diff --git a/src/personality.rs b/src/personality.rs
index 9e6dcc2..bfa2442 100644
--- a/src/personality.rs
+++ b/src/personality.rs
@@ -99,7 +99,7 @@ impl Game {
         if d > 1.1 {
             if e.path.is_empty() || e.repath <= 0.0 {
                 e.repath = 0.8;
-                if let Some(p) = self.map.path_to(e.tile(), idx(tx as i32, ty as i32)) {
+                if let Some(p) = self.map.creature_path(flies(e.kind), e.tile(), idx(tx as i32, ty as i32)) {
                     e.path = p;
                 }
             }
diff --git a/src/rival.rs b/src/rival.rs
index cedac10..aa72472 100644
--- a/src/rival.rs
+++ b/src/rival.rs
@@ -366,7 +366,7 @@ impl Game {
             e.repath = 1.5;
             // attackers dig their way like heroes; the player's creatures only walk
             let goal = |i: usize| self.target_core_adjacent(i, target);
-            let found = if e.side() == 0 { self.map.search(cur, self.map.walk_cost(), goal, true) } else { self.map.search(cur, self.map.hero_cost(), goal, true) };
+            let found = if e.side() == 0 { self.map.search(cur, self.map.creature_cost(flies(e.kind)), goal, true) } else { self.map.search(cur, self.map.hero_cost_as(flies(e.kind)), goal, true) };
             match found {
                 Some(p) => e.path = p,
                 None => {
@@ -411,7 +411,7 @@ impl Game {
             e.repath = 3.0 + self.rng.f() * 3.0;
             let (tx, ty) = if d2 > 36.0 { (hx, hy) } else { (hx + self.rng.f() * 8.0 - 4.0, hy + self.rng.f() * 8.0 - 4.0) };
             if self.map.walk(tx as i32, ty as i32) {
-                if let Some(p) = self.map.path_to(e.tile(), idx(tx as i32, ty as i32)) {
+                if let Some(p) = self.map.creature_path(flies(e.kind), e.tile(), idx(tx as i32, ty as i32)) {
                     e.path = p;
                 }
             }
diff --git a/src/traps.rs b/src/traps.rs
index a88750c..a04c9ae 100644
--- a/src/traps.rs
+++ b/src/traps.rs
@@ -263,7 +263,7 @@ impl Game {
             CRATED => {
                 if cur != crate_tile {
                     if e.path.is_empty() {
-                        match self.map.path_to(cur, crate_tile) {
+                        match self.map.creature_path(flies(e.kind), cur, crate_tile) {
                             Some(p) => e.path = p,
                             None => {
                                 self.traps[k].carrier = 0;
@@ -279,7 +279,7 @@ impl Game {
             CARRIED => {
                 if cur != tile {
                     if e.path.is_empty() {
-                        match self.map.path_to(cur, tile) {
+                        match self.map.creature_path(flies(e.kind), cur, tile) {
                             Some(p) => e.path = p,
                             None => {
                                 // no way there: the crate goes back into the forge