diff --git a/NEWS b/NEWS
index 47cd487cc..343c36543 100644
--- a/NEWS
+++ b/NEWS
@@ -5,6 +5,11 @@ New in spot 2.12.0.dev (not yet released)
   - Generating random formula without any unary opertors would very
     often create formulas much smaller than asked.
 
+  - The parity game solver, which internally works on "parity max
+    odd", but actually accept any type of parity acceptance, could be
+    confused by games with "parity min" acceptance using transition
+    with several colors (a rather uncommon situation).
+
 New in spot 2.12  (2024-05-16)
 
   Build:
diff --git a/spot/twaalgos/game.cc b/spot/twaalgos/game.cc
index 404fa4778..e2c550531 100644
--- a/spot/twaalgos/game.cc
+++ b/spot/twaalgos/game.cc
@@ -357,7 +357,8 @@ namespace spot
         // Takes an edge and returns the "equivalent" max odd parity
         auto equiv_par = [max, odd, next_max_par, inv = 2*max-1](const auto& e)
           {
-            par_t e_par = e.acc.max_set() - 1; // -1 for empty
+            par_t e_par =
+              (max ? e.acc.max_set() : e.acc.min_set()) - 1; // -1 for empty
             // If "min" and empty -> set to n
             if (!max & (e_par == -1))
               e_par = next_max_par;
diff --git a/tests/python/game.py b/tests/python/game.py
index e0d880647..3eba9bf41 100644
--- a/tests/python/game.py
+++ b/tests/python/game.py
@@ -351,6 +351,21 @@ State: 17
 --END--"""
 )
 
+def maximize_colors(aut, is_max):
+    ns = aut.num_sets()
+    v = []
+    if is_max:
+        for c in range(ns+1):
+            v.append(spot.mark_t(list(range(c))))
+        for e in aut.edges():
+            e.acc = v[e.acc.max_set()]
+    else:
+        for c in range(ns+1):
+            v.append(spot.mark_t(list(range(c, ns))))
+        v.insert(0, spot.mark_t([]))
+        for e in aut.edges():
+            e.acc = v[e.acc.min_set()]
+
 # Test the different parity conditions
 gdpa = spot.tgba_determinize(spot.degeneralize_tba(g),
                              False, True, True, False)
@@ -370,6 +385,14 @@ for kind in [spot.parity_kind_min, spot.parity_kind_max]:
         tc.assertTrue(spot.solve_parity_game(g_test_split1))
         c_strat1 = spot.get_strategy(g_test_split1)
         tc.assertTrue(c_strat == c_strat1)
+        # Same test, but adding a lot of useless colors in the game
+        g_test_split2 = spot.change_parity(g_test_split, kind, style)
+        maximize_colors(g_test_split2, kind == spot.parity_kind_max)
+        spot.set_state_players(g_test_split2, sp)
+        tc.assertTrue(spot.solve_parity_game(g_test_split2))
+        c_strat2 = spot.get_strategy(g_test_split2)
+        tc.assertTrue(c_strat == c_strat2)
+
 
 # Test that strategies are not appended
 # if solve is called multiple times
@@ -520,4 +543,4 @@ f1 = "((((G (F (idle))) && (G (((idle) && (X ((! (grant_0)) \
       && (! (F (G ((request_0) && (X (! (grant_0)))))))) \
       && (! (F (G ((request_1) && (X (! (grant_1)))))))))"
 outs = ["grant_0", "grant1"]
-tc.assertEqual(synt_ltlf(f1, outs)[0], False)
\ No newline at end of file
+tc.assertEqual(synt_ltlf(f1, outs)[0], False)