diff --git a/spot/twaalgos/postproc.cc b/spot/twaalgos/postproc.cc
index 1142220d7..3da54a67e 100644
--- a/spot/twaalgos/postproc.cc
+++ b/spot/twaalgos/postproc.cc
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2012-2020 Laboratoire de Recherche et Développement
+// Copyright (C) 2012-2021 Laboratoire de Recherche et Développement
 // de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
@@ -208,6 +208,8 @@ namespace spot
   twa_graph_ptr
   postprocessor::finalize(twa_graph_ptr tmp) const
   {
+    if (PREF_ != Any && level_ != Low)
+      tmp->remove_unused_ap();
     if (COMP_)
       tmp = complete(tmp);
     bool want_parity = type_ & Parity;
@@ -364,7 +366,6 @@ namespace spot
                 if (m->num_states() <= a->num_states())
                   a = m;
               }
-            a->remove_unused_ap();
           }
         return finalize(a);
       }
@@ -666,8 +667,6 @@ namespace spot
 
     sim = dba ? dba : sim;
 
-    sim->remove_unused_ap();
-
     if (type_ == CoBuchi)
       {
         unsigned ns = sim->num_states();
diff --git a/spot/twaalgos/translate.cc b/spot/twaalgos/translate.cc
index eb838e7b5..4db8643f9 100644
--- a/spot/twaalgos/translate.cc
+++ b/spot/twaalgos/translate.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2013-2018, 2020 Laboratoire de Recherche et Développement
-// de l'Epita (LRDE).
+// Copyright (C) 2013-2018, 2020-2021 Laboratoire de Recherche et
+// Développement de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
 //
@@ -383,17 +383,14 @@ namespace spot
                      || type_ == GeneralizedBuchi)
                   aut2 = gf_guarantee_to_ba_maybe(r, simpl_->get_dict(),
                                                   det, state_based_);
-                if (aut2 && (type_ & (Buchi | Parity))
-                    && (pref_ & Deterministic))
+                if (aut2 && (pref_ & Deterministic))
                   return finalize(aut2);
                 if (!aut2 && (type_ == Generic
                               || type_ & (Parity | CoBuchi)))
                   {
                     aut2 = fg_safety_to_dca_maybe(r, simpl_->get_dict(),
                                                   state_based_);
-                    if (aut2
-                        && (type_ & (CoBuchi | Parity))
-                        && (pref_ & Deterministic))
+                    if (aut2 && (pref_ & Deterministic))
                       return finalize(aut2);
                   }
               }
diff --git a/tests/core/ltl2tgba2.test b/tests/core/ltl2tgba2.test
index de6a9dc27..7e512c17a 100755
--- a/tests/core/ltl2tgba2.test
+++ b/tests/core/ltl2tgba2.test
@@ -1,6 +1,6 @@
 #!/bin/sh
 # -*- coding: utf-8 -*-
-# Copyright (C) 2009-2020 Laboratoire de Recherche et Développement de
+# Copyright (C) 2009-2021 Laboratoire de Recherche et Développement de
 # l'Epita (LRDE).
 # Copyright (C) 2003, 2004 Laboratoire d'Informatique de Paris 6 (LIP6),
 # département Systèmes Répartis Coopératifs (SRC), Université Pierre
@@ -376,8 +376,8 @@ cat >formulas <<EOF
 GF((a & XXa) | (!a & XX!a)), 4,8, 4,8, 6,14, 7,14, 4,8
 GF((a & XXXa) | (!a & XXX!a)), 7,14, 8,16, 8,18, 15,30, 8,16
 GF(((a & Xb) | XXc) & Xd), 3,58, 4,64, 3,58, 5,80, 4,64
-GF((b | Fa) & (b R Xb)), 2,4, 2,4, 3,6, 3,12, 2,4
-G(F(a & Xa) & F(a & X!a)), 2,4, 2,4, 4,8, 4,8, 3,6
+GF((b | Fa) & (b R Xb)), 2,4, 2,4, 3,6, 3,6, 2,4
+G(F(a & Xa) & F(a & X!a)), 2,4, 2,4, 4,8, 4,8, 2,4
 G(!p0 & F(p1 & XG!p1)), 1,0, 1,0, 1,0, 1,0, 1,0
 FG(a | Fb), 3,15, 3,15, 3,15, 3,15, 1,4
 FG(a & Fb), 2,7, 2,7, 3,9, 3,9, 1,4
diff --git a/tests/core/prodor.test b/tests/core/prodor.test
index 73bcf6a91..03127508b 100755
--- a/tests/core/prodor.test
+++ b/tests/core/prodor.test
@@ -1,7 +1,7 @@
 #!/bin/sh
 # -*- coding: utf-8 -*-
-# Copyright (C) 2015, 2017, 2018 Laboratoire de Recherche et Développement
-# de l'Epita (LRDE).
+# Copyright (C) 2015, 2017-2018, 2021 Laboratoire de Recherche et
+# Développement de l'Epita (LRDE).
 #
 # This file is part of Spot, a model checking library.
 #
@@ -63,21 +63,21 @@ properties: trans-labels explicit-labels trans-acc complete
 properties: stutter-invariant
 --BODY--
 State: 0
-[!0] 0
 [0] 0 {0}
+[!0] 0
+[0&1] 1 {0}
 [!0&1] 1
-[0&1] 1 {0}
 State: 1
-[!0&1] 1 {0}
 [0&1] 1 {0}
-[!0&!1] 2 {0}
+[!0&1] 1 {0}
 [0&!1] 2 {0}
+[!0&!1] 2 {0}
 State: 2
-[!0] 2
 [0] 2 {0}
+[!0] 2
 --END--
 EOF
-diff por.hoa exp
+diff -u por.hoa exp
 
 test 2 = `autfilt -c --intersect por.hoa gfa.hoa fgb.hoa`
 
@@ -94,13 +94,13 @@ Acceptance: 1 Inf(0)
 properties: trans-labels explicit-labels trans-acc stutter-invariant
 --BODY--
 State: 0
-[!0] 0
 [0] 0
-[!0&1] 1
+[!0] 0
 [0&1] 1
-State: 1
 [!0&1] 1
+State: 1
 [0&1] 1 {0}
+[!0&1] 1
 --END--
 EOF
 diff pand.hoa exp
diff --git a/tests/python/automata.ipynb b/tests/python/automata.ipynb
index 6b62441fa..757538838 100644
--- a/tests/python/automata.ipynb
+++ b/tests/python/automata.ipynb
@@ -178,7 +178,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc69c0f16c0> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43cde71b0> >"
       ]
      },
      "execution_count": 2,
@@ -657,7 +657,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc68d909240> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43c131fc0> >"
       ]
      },
      "execution_count": 6,
@@ -733,7 +733,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc68d9099c0> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43c1563c0> >"
       ]
      },
      "execution_count": 7,
@@ -816,7 +816,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc69e19d9c0> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43c131ba0> >"
       ]
      },
      "execution_count": 8,
@@ -1349,7 +1349,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc68d916150> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43c156e40> >"
       ]
      },
      "execution_count": 12,
@@ -1463,7 +1463,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc68d916450> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43c163300> >"
       ]
      },
      "execution_count": 13,
@@ -1594,7 +1594,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc68d916a20> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43c163810> >"
       ]
      },
      "execution_count": 14,
@@ -1816,7 +1816,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc68d91ca20> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43c1694b0> >"
       ]
      },
      "metadata": {},
@@ -1974,7 +1974,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc68d91c9c0> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43c163210> >"
       ]
      },
      "metadata": {},
@@ -2132,7 +2132,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc68d91cd80> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43c169180> >"
       ]
      },
      "metadata": {},
@@ -2280,7 +2280,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc68d91ccc0> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43c169360> >"
       ]
      },
      "metadata": {},
@@ -2469,7 +2469,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc68d91cb40> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43c169210> >"
       ]
      },
      "execution_count": 19,
@@ -2545,7 +2545,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc68d925690> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43c169fc0> >"
       ]
      },
      "execution_count": 20,
@@ -3095,7 +3095,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc68d91c480> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43c156ea0> >"
       ]
      },
      "metadata": {},
@@ -3195,7 +3195,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc68d91c510> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43c156210> >"
       ]
      },
      "execution_count": 24,
@@ -3254,21 +3254,21 @@
        "<title>0&#45;&gt;0</title>\n",
        "<path fill=\"none\" stroke=\"black\" d=\"M55.26,-35.78C54.71,-45.31 55.79,-54 58.5,-54 60.49,-54 61.6,-49.32 61.83,-43.05\"/>\n",
        "<polygon fill=\"black\" stroke=\"black\" points=\"61.74,-35.78 64.98,-42.74 61.78,-39.28 61.83,-42.78 61.83,-42.78 61.83,-42.78 61.78,-39.28 58.68,-42.82 61.74,-35.78 61.74,-35.78\"/>\n",
-       "<text text-anchor=\"start\" x=\"55\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
+       "<text text-anchor=\"start\" x=\"53\" y=\"-72.8\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
+       "<text text-anchor=\"start\" x=\"50.5\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
        "</g>\n",
        "<!-- 0&#45;&gt;0 -->\n",
        "<g id=\"edge3\" class=\"edge\">\n",
        "<title>0&#45;&gt;0</title>\n",
-       "<path fill=\"none\" stroke=\"black\" d=\"M53.18,-35.42C50.15,-52.79 51.93,-72 58.5,-72 64.2,-72 66.29,-57.55 64.77,-42.39\"/>\n",
-       "<polygon fill=\"black\" stroke=\"black\" points=\"63.82,-35.42 67.89,-41.93 64.29,-38.89 64.76,-42.36 64.76,-42.36 64.76,-42.36 64.29,-38.89 61.64,-42.78 63.82,-35.42 63.82,-35.42\"/>\n",
-       "<text text-anchor=\"start\" x=\"53\" y=\"-90.8\" font-family=\"Lato\" font-size=\"14.00\">!a</text>\n",
-       "<text text-anchor=\"start\" x=\"50.5\" y=\"-75.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M53.49,-35.58C50.05,-56.72 51.71,-84 58.5,-84 64.54,-84 66.53,-62.36 64.46,-42.69\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"63.51,-35.58 67.56,-42.1 63.97,-39.05 64.43,-42.52 64.43,-42.52 64.43,-42.52 63.97,-39.05 61.31,-42.93 63.51,-35.58 63.51,-35.58\"/>\n",
+       "<text text-anchor=\"start\" x=\"55\" y=\"-87.8\" font-family=\"Lato\" font-size=\"14.00\">a</text>\n",
        "</g>\n",
        "</g>\n",
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc68d91c2d0> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe440654c60> >"
       ]
      },
      "execution_count": 25,
@@ -3439,7 +3439,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc68d9164e0> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43c1316c0> >"
       ]
      },
      "execution_count": 27,
@@ -3522,7 +3522,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc68d91c480> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43c156ea0> >"
       ]
      },
      "metadata": {},
@@ -3587,7 +3587,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc68d91c480> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43c156ea0> >"
       ]
      },
      "metadata": {},
@@ -3674,7 +3674,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc68d91c480> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fe43c156ea0> >"
       ]
      },
      "execution_count": 29,
@@ -3707,7 +3707,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.6"
+   "version": "3.9.1+"
   }
  },
  "nbformat": 4,
diff --git a/tests/python/toparity.py b/tests/python/toparity.py
index a7b034f21..eebadfdd3 100644
--- a/tests/python/toparity.py
+++ b/tests/python/toparity.py
@@ -1,6 +1,6 @@
 #!/usr/bin/python3
 # -*- mode: python; coding: utf-8 -*-
-# Copyright (C) 2018-2020 Laboratoire de Recherche et Développement de
+# Copyright (C) 2018-2021 Laboratoire de Recherche et Développement de
 # l'EPITA.
 #
 # This file is part of Spot, a model checking library.
@@ -112,7 +112,7 @@ def test(aut, expected_num_states=[], full=True):
             spot.reduce_parity_here(p1)
         assert spot.are_equivalent(aut, p1)
         if expected_num is not None:
-            # print(p1.num_states(), expected_num)
+            print(p1.num_states(), expected_num)
             assert p1.num_states() == expected_num
         if full:
             # Make sure passing opt is the same as setting
@@ -391,4 +391,4 @@ for f in spot.randltl(5, 2000):
 a = spot.translate('!(GFa -> (GFb & GF(!b & !Xb)))', 'gen', 'det')
 b = spot.to_parity_old(a, True)
 assert a.equivalent_to(b)
-test(a, [7, 7, 3, 7, 8, 7, 3])
+test(a, [7, 7, 3, 7, 7, 7, 3])