diff --git a/src/board.rs b/src/board.rs
index a23adf5..19435c7 100644
--- a/src/board.rs
+++ b/src/board.rs
@@ -363,11 +363,18 @@ impl Board {
         self.transform(Bitboard::rotate_270);
     }
 
-    /// Makes black pieces white and vice versa.
+    /// Swap piece colors, making black pieces white and vice versa.
     pub fn swap_colors(&mut self) {
         self.by_color.swap();
     }
 
+    /// Mirror the board vertically and swap piece colors, so that the resulting
+    /// board is equivalent modulo color.
+    pub fn mirror(&mut self) {
+        self.flip_vertical();
+        self.swap_colors();
+    }
+
     pub fn pop_front(&mut self) -> Option<(Square, Piece)> {
         self.occupied
             .first()
diff --git a/src/position.rs b/src/position.rs
index 126ad89..dae0276 100644
--- a/src/position.rs
+++ b/src/position.rs
@@ -633,7 +633,8 @@ pub trait Position {
         }
     }
 
-    /// Swap turns. This is sometimes called "playing a null move".
+    /// Swap turns and discard en passant rights. This is sometimes called
+    /// "playing a null move".
     ///
     /// # Errors
     ///
diff --git a/src/setup.rs b/src/setup.rs
index 6b27f01..dba671f 100644
--- a/src/setup.rs
+++ b/src/setup.rs
@@ -110,11 +110,31 @@ impl Setup {
         }
     }
 
+    /// Swap turns and discard en passant rights. This is sometimes called
+    /// "playing a null move".
     pub fn swap_turn(&mut self) {
         self.turn = !self.turn;
         self.ep_square = None;
     }
 
+    /// Mirror vertically and swap turns and all piece colors, so that the
+    /// resulting setup is equivalent modulo color.
+    ///
+    /// Move counters remain unchanged.
+    pub fn mirror(&mut self) {
+        self.board.mirror();
+        self.promoted = self.promoted.flip_vertical();
+        if let Some(pockets) = &mut self.pockets {
+            pockets.swap();
+        }
+        self.turn = !self.turn;
+        self.castling_rights = self.castling_rights.flip_vertical();
+        self.ep_square = self.ep_square.map(Square::flip_vertical);
+        if let Some(remaining_checks) = &mut self.remaining_checks {
+            remaining_checks.swap();
+        }
+    }
+
     pub fn position<P: FromSetup>(self, mode: CastlingMode) -> Result<P, PositionError<P>> {
         P::from_setup(self, mode)
     }