diff --git a/spot/twaalgos/determinize.cc b/spot/twaalgos/determinize.cc
index 323a5ad0d..f6b418b17 100644
--- a/spot/twaalgos/determinize.cc
+++ b/spot/twaalgos/determinize.cc
@@ -26,7 +26,6 @@
 #include <set>
 #include <map>
 
-
 #include <spot/misc/bddlt.hh>
 #include <spot/twaalgos/sccinfo.hh>
 #include <spot/twaalgos/determinize.hh>
@@ -34,7 +33,7 @@
 #include <spot/twaalgos/sccfilter.hh>
 #include <spot/twaalgos/simulation.hh>
 #include <spot/twaalgos/isdet.hh>
-
+#include <spot/twaalgos/parity.hh>
 
 namespace spot
 {
@@ -448,15 +447,6 @@ namespace spot
       return res;
     }
 
-    // Used to remove all acceptance whose value is above or equal to max_acc
-    void remove_dead_acc(twa_graph_ptr& aut, unsigned max_acc)
-    {
-      assert(max_acc < 32);
-      unsigned mask = (1 << max_acc) - 1;
-      for (auto& t: aut->edges())
-        t.acc &= mask;
-    }
-
     struct compare
     {
       bool
@@ -961,20 +951,23 @@ namespace spot
             if (s.color_ != -1U)
               {
                 res->new_edge(src_num, dst_num, s.cond(), {s.color_});
-                // We only care about green acc which are odd
-                if (s.color_ % 2 == 1)
-                  sets = std::max(s.color_ + 1, sets);
+                sets = std::max(s.color_ + 1, sets);
               }
             else
               res->new_edge(src_num, dst_num, s.cond());
           }
       }
-    remove_dead_acc(res, sets);
+    // Green and red colors work in pairs, so the number of parity conditions is
+    // necessarily even.
+    if (sets % 2 == 1)
+      sets += 1;
     // Acceptance is now min(odd) since we can emit Red on paths 0 with new opti
     res->set_acceptance(sets, acc_cond::acc_code::parity(false, true, sets));
     res->prop_universal(true);
     res->prop_state_acc(false);
 
+    cleanup_parity_here(res);
+
     if (pretty_print)
       res->set_named_prop("state-names", print_debug(aut, seen));
     return res;
diff --git a/tests/core/safra.test b/tests/core/safra.test
index 85a304911..c5b2277ff 100755
--- a/tests/core/safra.test
+++ b/tests/core/safra.test
@@ -45,15 +45,15 @@ HOA: v1
 States: 4
 Start: 0
 AP: 2 "a" "b"
-acc-name: Rabin 1
-Acceptance: 2 Fin(0) & Inf(1)
+acc-name: Buchi
+Acceptance: 1 Inf(0)
 properties: trans-labels explicit-labels trans-acc deterministic
 --BODY--
 State: 0
 [0] 1
 State: 1
 [!0&1] 2
-[0] 3 {1}
+[0] 3 {0}
 State: 2
 [0&!1] 0
 [!0&1] 2
@@ -90,27 +90,27 @@ HOA: v1
 States: 5
 Start: 0
 AP: 2 "a" "b"
-acc-name: Rabin 1
-Acceptance: 2 Fin(0) & Inf(1)
+acc-name: Buchi
+Acceptance: 1 Inf(0)
 properties: trans-labels explicit-labels trans-acc deterministic
 --BODY--
 State: 0
 [0] 1
 State: 1
 [0&!1] 1
-[!0&1] 2 {1}
+[!0&1] 2 {0}
 [0&1] 3
 State: 2
 [0&!1] 0
-[!0&1] 2 {1}
+[!0&1] 2 {0}
 [0&1] 3
 State: 3
-[0&1] 1 {1}
-[!0&1] 2 {1}
+[0&1] 1 {0}
+[!0&1] 2 {0}
 [0&!1] 4
 State: 4
-[0] 1 {1}
-[!0&1] 2 {1}
+[0] 1 {0}
+[!0&1] 2 {0}
 --END--
 EOF
 
diff --git a/tests/python/simstate.py b/tests/python/simstate.py
index ee014ebbe..e2bf5330e 100644
--- a/tests/python/simstate.py
+++ b/tests/python/simstate.py
@@ -1,5 +1,5 @@
 # -*- mode: python; coding: utf-8 -*-
-# Copyright (C) 2015, 2017  Laboratoire de Recherche et Développement
+# Copyright (C) 2015, 2017-2018  Laboratoire de Recherche et Développement
 # de l'Epita
 #
 # This file is part of Spot, a model checking library.
@@ -70,26 +70,26 @@ assert daut.to_str() == """HOA: v1
 States: 3
 Start: 0
 AP: 2 "p1" "p0"
-acc-name: parity min odd 4
-Acceptance: 4 Fin(0) & (Inf(1) | (Fin(2) & Inf(3)))
+acc-name: parity min even 3
+Acceptance: 3 Inf(0) | (Fin(1) & Inf(2))
 properties: trans-labels explicit-labels trans-acc complete
 properties: deterministic stutter-invariant
 --BODY--
 State: 0 "{₀[0]₀}"
 [!0&!1] 0
 [!0&1] 0
-[0&!1] 0 {1}
-[0&1] 1 {3}
+[0&!1] 0 {0}
+[0&1] 1 {2}
 State: 1 "{₀[0]{₂[2]₂}₀}{₁[1]₁}"
-[!0&!1] 0 {2}
+[!0&!1] 0 {1}
 [!0&1] 2
-[0&!1] 0 {1}
-[0&1] 1 {3}
+[0&!1] 0 {0}
+[0&1] 1 {2}
 State: 2 "{₀[0]₀}{₁[1]₁}"
-[!0&!1] 0 {2}
+[!0&!1] 0 {1}
 [!0&1] 2
-[0&!1] 0 {1}
-[0&1] 1 {3}
+[0&!1] 0 {0}
+[0&1] 1 {2}
 --END--"""
 
 aut = spot.automaton("""
@@ -113,8 +113,8 @@ assert daut.to_str() == """HOA: v1
 States: 12
 Start: 0
 AP: 2 "a" "b"
-acc-name: parity min odd 4
-Acceptance: 4 Fin(0) & (Inf(1) | (Fin(2) & Inf(3)))
+acc-name: Buchi
+Acceptance: 1 Inf(0)
 properties: trans-labels explicit-labels trans-acc deterministic
 --BODY--
 State: 0 "{₀[0#0,0#1]₀}"
@@ -123,7 +123,7 @@ State: 0 "{₀[0#0,0#1]₀}"
 [0&1] 2
 State: 1 "{₀[1#1]₀}"
 [!0&1] 0
-[0&!1] 3 {1}
+[0&!1] 3 {0}
 [0&1] 4
 State: 2 "{₀[0#0,0#1] [1#1]₀}"
 [!0&1] 2
@@ -147,24 +147,24 @@ State: 6 "{₀[0#0,0#1] [1#0]₀}"
 [0&1] 9
 State: 7 "{₀[1#1]{₁[0#0,0#1]₁}₀}"
 [!0&1] 10
-[0&!1] 6 {1}
-[0&1] 9 {1}
+[0&!1] 6 {0}
+[0&1] 9 {0}
 State: 8 "{₀[1#1]{₁[0#0,0#1] [1#0]₁}₀}"
-[!0&1] 2 {1}
-[0&!1] 6 {1}
-[0&1] 9 {1}
+[!0&1] 2 {0}
+[0&!1] 6 {0}
+[0&1] 9 {0}
 State: 9 "{₀[0#0,0#1] [1#1] [1#0]₀}"
 [!0&1] 2
 [0&!1] 4
 [0&1] 5
 State: 10 "{₀[0#0,0#1]{₁[1#1]₁}₀}"
 [!0&1] 7
-[0&!1] 4 {3}
+[0&!1] 4 {0}
 [0&1] 11
 State: 11 "{₀[1#1]{₁[0#0,0#1]{₂[1#0]₂}₁}₀}"
-[!0&1] 2 {1}
-[0&!1] 6 {1}
-[0&1] 9 {1}
+[!0&1] 2 {0}
+[0&!1] 6 {0}
+[0&1] 9 {0}
 --END--"""
 
 a = spot.translate('!Gp0 xor FG((p0 W Gp1) M p1)')