diff --git a/spot/twaalgos/game.cc b/spot/twaalgos/game.cc
index 3f041ac1c..419b33fe3 100644
--- a/spot/twaalgos/game.cc
+++ b/spot/twaalgos/game.cc
@@ -836,54 +836,63 @@ namespace spot
 
   void pg_print(std::ostream& os, const const_twa_graph_ptr& arena)
   {
-    auto owner = ensure_parity_game(arena, "pg_print");
-    // Ensure coloring
-    assert([&]()
-            {
-              bool max;
-              bool odd;
-              arena->acc().is_parity(max, odd, true);
-              return max && odd;
-            }() && "pg_printer needs max-odd parity");
-    assert([&]()
-           {
-             for (unsigned ie = 0; ie < arena->num_edges(); ++ie)
-               {
-                  const auto& es = arena->edge_storage(ie+1);
-                  if (!es.acc)
-                    return false;
-               }
-             return true;
-           }() && "Arena must be colorized");
+    ensure_parity_game(arena, "pg_print");
 
-    unsigned ns = arena->num_states();
-    unsigned init = arena->get_init_state_number();
-    os << "parity " << ns - 1 << ";\n";
-    std::vector<bool> seen(ns, false);
-    std::vector<unsigned> todo({init});
-    while (!todo.empty())
+    auto do_print = [&os](const const_twa_graph_ptr& arena)
       {
-        unsigned src = todo.back();
-        todo.pop_back();
-        if (seen[src])
-          continue;
-        seen[src] = true;
-        os << src << ' ';
-        os << arena->out(src).begin()->acc.max_set() - 1 << ' ';
-        os << (*owner)[src] << ' ';
-        bool first = true;
-        for (auto& e: arena->out(src))
+        const region_t& owner = get_state_players(arena);
+
+        unsigned ns = arena->num_states();
+        unsigned init = arena->get_init_state_number();
+        os << "parity " << ns - 1 << ";\n";
+        std::vector<bool> seen(ns, false);
+        std::vector<unsigned> todo({init});
+        while (!todo.empty())
           {
-            if (!first)
-              os << ',';
-            first = false;
-            os << e.dst;
-            if (!seen[e.dst])
-              todo.push_back(e.dst);
+            unsigned src = todo.back();
+            todo.pop_back();
+            if (seen[src])
+              continue;
+            seen[src] = true;
+            os << src << ' ';
+            os << arena->out(src).begin()->acc.max_set() - 1 << ' ';
+            os << owner[src] << ' ';
+            bool first = true;
+            for (auto& e: arena->out(src))
+              {
+                if (!first)
+                  os << ',';
+                first = false;
+                os << e.dst;
+                if (!seen[e.dst])
+                  todo.push_back(e.dst);
+              }
+            if (src == init)
+              os << " \"INIT\"";
+            os << ";\n";
           }
-        if (src == init)
-          os << " \"INIT\"";
-        os << ";\n";
+      };
+    // Ensure coloring
+    // PGSolver format expects max odd and colored
+    bool is_par, max, odd;
+    is_par = arena->acc().is_parity(max, odd, true);
+    assert(is_par && "pg_printer needs parity condition");
+    bool is_colored = (max & odd) ? std::all_of(arena->edges().begin(),
+                                              arena->edges().end(),
+                                              [](const auto& e)
+                                                {
+                                                  return (bool) e.acc;
+                                                })
+                                  : false;
+    if (is_colored)
+      do_print(arena);
+    else
+      {
+        auto arena2 = change_parity(arena, parity_kind_max, parity_style_odd);
+        colorize_parity_here(arena2, true);
+        set_state_players(arena2,
+                          get_state_players(arena));
+        do_print(arena2);
       }
   }
 
diff --git a/spot/twaalgos/synthesis.cc b/spot/twaalgos/synthesis.cc
index 5a5d1297a..41aa736e2 100644
--- a/spot/twaalgos/synthesis.cc
+++ b/spot/twaalgos/synthesis.cc
@@ -837,13 +837,10 @@ namespace spot
       if (force_sbacc)
         dpa = sbacc(dpa);
       reduce_parity_here(dpa, true);
-      change_parity_here(dpa, parity_kind_max,
-                               parity_style_odd);
       assert((
                  [&dpa]() -> bool {
                    bool max, odd;
-                   dpa->acc().is_parity(max, odd);
-                   return max && odd;
+                   return dpa->acc().is_parity(max, odd);
                  }()));
       assert(is_deterministic(dpa));
       return dpa;
@@ -936,7 +933,6 @@ namespace spot
         if (bv)
           sw.start();
         dpa = split_2step(tmp, outs, true);
-        colorize_parity_here(dpa, true);
         if (bv)
           bv->split_time += sw.stop();
         if (vs)
@@ -959,7 +955,6 @@ namespace spot
         if (bv)
           sw.start();
         dpa = split_2step(aut, outs, true);
-        colorize_parity_here(dpa, true);
         if (bv)
           bv->split_time += sw.stop();
         if (vs)
@@ -1031,8 +1026,6 @@ namespace spot
         if (bv)
           sw.start();
         dpa = split_2step(dpa, outs, true);
-        change_parity_here(dpa, parity_kind_max, parity_style_odd);
-        colorize_parity_here(dpa, true);
         if (bv)
           bv->split_time += sw.stop();
         if (vs)
diff --git a/tests/core/ltlsynt.test b/tests/core/ltlsynt.test
index 9319d96a8..6cb449012 100644
--- a/tests/core/ltlsynt.test
+++ b/tests/core/ltlsynt.test
@@ -232,7 +232,7 @@ LAR construction done in X seconds
 DPA has 4 states, 1 colors
 split inputs and outputs done in X seconds
 automaton has 12 states
-solving game with acceptance: parity max odd 3
+solving game with acceptance: co-Büchi
 game solved in X seconds
 EOF
 ltlsynt -f "G(Fi0 && Fi1 && Fi2) -> G(i1 <-> o0)" --outs="o0" --algo=lar \
@@ -708,7 +708,7 @@ LAR construction done in X seconds
 DPA has 4 states, 1 colors
 split inputs and outputs done in X seconds
 automaton has 9 states
-solving game with acceptance: Streett 1
+solving game with acceptance: Büchi
 game solved in X seconds
 simplification took X seconds
 AIG circuit was created in X seconds and has 0 latches and 0 gates
@@ -727,7 +727,7 @@ LAR construction done in X seconds
 DPA has 2 states, 0 colors
 split inputs and outputs done in X seconds
 automaton has 4 states
-solving game with acceptance: Streett 1
+solving game with acceptance: all
 game solved in X seconds
 simplification took X seconds
 trying to create strategy directly for (a | x) -> x
@@ -738,7 +738,7 @@ LAR construction done in X seconds
 DPA has 2 states, 0 colors
 split inputs and outputs done in X seconds
 automaton has 4 states
-solving game with acceptance: Streett 1
+solving game with acceptance: all
 game solved in X seconds
 simplification took X seconds
 AIG circuit was created in X seconds and has 0 latches and 0 gates
@@ -797,7 +797,7 @@ LAR construction done in X seconds
 DPA has 2 states, 1 colors
 split inputs and outputs done in X seconds
 automaton has 5 states
-solving game with acceptance: Streett 1
+solving game with acceptance: Büchi
 game solved in X seconds
 simplification took X seconds
 AIG circuit was created in X seconds and has 0 latches and 0 gates
@@ -819,7 +819,7 @@ LAR construction done in X seconds
 DPA has 2 states, 0 colors
 split inputs and outputs done in X seconds
 automaton has 4 states
-solving game with acceptance: Streett 1
+solving game with acceptance: all
 game solved in X seconds
 simplification took X seconds
 trying to create strategy directly for a -> c
@@ -830,7 +830,7 @@ LAR construction done in X seconds
 DPA has 2 states, 0 colors
 split inputs and outputs done in X seconds
 automaton has 4 states
-solving game with acceptance: Streett 1
+solving game with acceptance: all
 game solved in X seconds
 simplification took X seconds
 trying to create strategy directly for a -> d
@@ -841,7 +841,7 @@ LAR construction done in X seconds
 DPA has 2 states, 0 colors
 split inputs and outputs done in X seconds
 automaton has 4 states
-solving game with acceptance: Streett 1
+solving game with acceptance: all
 game solved in X seconds
 simplification took X seconds
 AIG circuit was created in X seconds and has 0 latches and 0 gates
@@ -903,7 +903,7 @@ LAR construction done in X seconds
 DPA has 1 states, 0 colors
 split inputs and outputs done in X seconds
 automaton has 2 states
-solving game with acceptance: Streett 1
+solving game with acceptance: all
 game solved in X seconds
 translating formula done in X seconds
 automaton has 2 states and 2 colors
@@ -911,7 +911,7 @@ LAR construction done in X seconds
 DPA has 2 states, 2 colors
 split inputs and outputs done in X seconds
 automaton has 5 states
-solving game with acceptance: parity max odd 4
+solving game with acceptance: Streett 1
 game solved in X seconds
 EOF
 
@@ -927,7 +927,7 @@ ACD construction done in X seconds
 DPA has 2 states, 2 colors
 split inputs and outputs done in X seconds
 automaton has 6 states
-solving game with acceptance: parity max odd 4
+solving game with acceptance: generalized-Streett 1 1
 game solved in X seconds
 simplification took X seconds
 translating formula done in X seconds
@@ -936,7 +936,7 @@ ACD construction done in X seconds
 DPA has 1 states, 0 colors
 split inputs and outputs done in X seconds
 automaton has 2 states
-solving game with acceptance: Streett 1
+solving game with acceptance: all
 game solved in X seconds
 simplification took X seconds
 EOF
@@ -959,7 +959,7 @@ LAR construction done in X seconds
 DPA has 1 states, 1 colors
 split inputs and outputs done in X seconds
 automaton has 3 states
-solving game with acceptance: Streett 1
+solving game with acceptance: Büchi
 game solved in X seconds
 EOF
 ltlsynt -f "G(o1) & (GFi <-> GFo1)" --outs="o1" --verbose\
@@ -977,7 +977,7 @@ LAR construction done in X seconds
 DPA has 2 states, 2 colors
 split inputs and outputs done in X seconds
 automaton has 6 states
-solving game with acceptance: parity max odd 4
+solving game with acceptance: Streett 1
 game solved in X seconds
 simplification took X seconds
 EOF
diff --git a/tests/python/_mealy.ipynb b/tests/python/_mealy.ipynb
index 4e7374852..c2aeb125c 100644
--- a/tests/python/_mealy.ipynb
+++ b/tests/python/_mealy.ipynb
@@ -65,78 +65,70 @@
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-       "<text text-anchor=\"start\" x=\"70.5\" y=\"-175.87\" font-family=\"Lato\" font-size=\"14.00\">[Streett 1]</text>\n",
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        "</g>\n",
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f32ec50ce40> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc1244a3d50> >"
       ]
      },
      "execution_count": 4,
@@ -216,7 +208,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f32ec571c30> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc124439570> >"
       ]
      },
      "execution_count": 6,
@@ -290,7 +282,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f32ec571c30> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc124439570> >"
       ]
      },
      "execution_count": 8,
@@ -301,6 +293,14 @@
    "source": [
     "x"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "923a59d6",
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
@@ -319,7 +319,7 @@
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diff --git a/tests/python/games.ipynb b/tests/python/games.ipynb
index ac3490b2b..891ebcd94 100644
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-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f202420db10> >"
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       "States: 12\n",
       "Start: 4\n",
       "AP: 2 \"b\" \"a\"\n",
-      "acc-name: parity max odd 3\n",
-      "Acceptance: 3 Fin(2) & (Inf(1) | Fin(0))\n",
-      "properties: trans-labels explicit-labels trans-acc colored complete\n",
+      "acc-name: co-Buchi\n",
+      "Acceptance: 1 Fin(0)\n",
+      "properties: trans-labels explicit-labels trans-acc complete\n",
       "properties: deterministic\n",
       "spot-state-player: 0 0 0 0 0 1 1 1 1 1 1 1\n",
       "controllable-AP: 0\n",
       "--BODY--\n",
       "State: 0\n",
-      "[!1] 5 {1}\n",
-      "[1] 6 {2}\n",
+      "[!1] 5\n",
+      "[1] 6 {0}\n",
       "State: 1\n",
-      "[1] 6 {2}\n",
-      "[!1] 7 {2}\n",
+      "[1] 6 {0}\n",
+      "[!1] 7 {0}\n",
       "State: 2\n",
-      "[t] 8 {1}\n",
+      "[t] 8\n",
       "State: 3\n",
-      "[t] 9 {1}\n",
+      "[t] 9\n",
       "State: 4\n",
-      "[!1] 10 {1}\n",
-      "[1] 11 {1}\n",
+      "[!1] 10\n",
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-      "[t] 0 {1}\n",
+      "[t] 0\n",
       "State: 6\n",
-      "[t] 1 {2}\n",
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       "State: 7\n",
-      "[t] 0 {2}\n",
+      "[t] 0 {0}\n",
       "State: 8\n",
-      "[t] 2 {1}\n",
+      "[t] 2\n",
       "State: 9\n",
-      "[!0] 2 {1}\n",
-      "[0] 3 {2}\n",
+      "[!0] 2\n",
+      "[0] 3 {0}\n",
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-      "[!0] 0 {1}\n",
-      "[0] 3 {1}\n",
+      "[!0] 0\n",
+      "[0] 3\n",
       "State: 11\n",
-      "[!0] 1 {1}\n",
-      "[0] 3 {1}\n",
+      "[!0] 1\n",
+      "[0] 3\n",
       "--END--\n"
      ]
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diff --git a/tests/python/synthesis.ipynb b/tests/python/synthesis.ipynb
index 08af437e2..3e8b4f5ea 100644
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@@ -3939,7 +3801,7 @@
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       ],
       "text/plain": [
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       ],
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@@ -4117,7 +3979,7 @@
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       ],
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@@ -4297,7 +4159,7 @@
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@@ -4421,7 +4283,7 @@
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       "text/plain": [
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+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc968069ed0> >"
       ]
      },
      "execution_count": 16,
diff --git a/tests/python/synthesis.py b/tests/python/synthesis.py
index 559dc2d24..98ac889d8 100644
--- a/tests/python/synthesis.py
+++ b/tests/python/synthesis.py
@@ -35,18 +35,18 @@ tc.assertEqual(game.to_str(), """HOA: v1
 States: 3
 Start: 0
 AP: 1 "a"
-acc-name: Streett 1
-Acceptance: 2 Fin(0) | Inf(1)
-properties: trans-labels explicit-labels trans-acc colored complete
+acc-name: Buchi
+Acceptance: 1 Inf(0)
+properties: trans-labels explicit-labels trans-acc complete
 properties: deterministic
 spot-state-player: 0 1 1
 controllable-AP:
 --BODY--
 State: 0
-[!0] 1 {0}
-[0] 2 {1}
+[!0] 1
+[0] 2 {0}
 State: 1
-[t] 0 {0}
+[t] 0
 State: 2
-[t] 0 {1}
+[t] 0 {0}
 --END--""")