diff --git a/spot/twaalgos/cleanacc.cc b/spot/twaalgos/cleanacc.cc
index 685507112..87a42917c 100644
--- a/spot/twaalgos/cleanacc.cc
+++ b/spot/twaalgos/cleanacc.cc
@@ -617,20 +617,20 @@ namespace spot
 
   twa_graph_ptr simplify_acceptance_here(twa_graph_ptr aut)
   {
-    cleanup_acceptance_here(aut, false);
-    merge_identical_marks_here(aut);
-    if (!aut->acc().is_generalized_buchi())
+    for (;;)
       {
+        cleanup_acceptance_here(aut, false);
+        merge_identical_marks_here(aut);
+        if (aut->acc().is_generalized_buchi())
+          break;
+        acc_cond::acc_code old = aut->get_acceptance();
         simplify_complementary_marks_here(aut);
         fuse_marks_here(aut);
+        aut->set_acceptance(aut->acc().unit_propagation());
+        if (old == aut->get_acceptance())
+          break;
       }
     cleanup_acceptance_here(aut, true);
-    auto prop_cond = aut->acc().unit_propagation();
-    if (prop_cond != aut->acc())
-    {
-      aut->set_acceptance(prop_cond);
-      cleanup_acceptance_here(aut, true);
-    }
     return aut;
   }
 
diff --git a/tests/core/accsimpl.test b/tests/core/accsimpl.test
index 17404023f..1dbf06095 100755
--- a/tests/core/accsimpl.test
+++ b/tests/core/accsimpl.test
@@ -72,4 +72,4 @@ State: 0
 --END--
 EOF
 autcross --language-preserved 'autfilt --simplify-acc' -F frenkin
-test 1,4,2 = "`autfilt --simplify-acc frenkin --stats=%s,%e,%a`"
+test 1,4,1 = "`autfilt --simplify-acc frenkin --stats=%s,%e,%a`"
diff --git a/tests/core/remfin.test b/tests/core/remfin.test
index 0b387d8e0..c8b1eb670 100755
--- a/tests/core/remfin.test
+++ b/tests/core/remfin.test
@@ -313,27 +313,25 @@ State: 2 {0}
 [!1] 2
 --END--
 HOA: v1
-States: 4
+States: 3
 Start: 0
 AP: 2 "a" "b"
-Acceptance: 4 Inf(0) | Inf(3) | (Inf(1)&Inf(2))
+acc-name: Buchi
+Acceptance: 1 Inf(0)
 properties: trans-labels explicit-labels trans-acc
 --BODY--
 State: 0
-[t] 0 {2 3}
-[0] 1 {2 3}
-[!0] 2 {2 3}
+[t] 0 {0}
+[0] 1 {0}
+[!0] 2 {0}
 State: 1
-[1] 0 {2}
-[0&1] 1 {2}
-[!0&1] 2 {1 2}
+[1] 0 {0}
+[0&1] 1 {0}
+[!0&1] 2 {0}
 State: 2
 [!1] 0
-[0&!1] 1
-[!0&!1] 2
-[!0&!1] 3
-State: 3
-[!0&!1] 3 {0}
+[0&!1] 1 {0}
+[!0&!1] 2 {0}
 --END--
 HOA: v1
 States: 3
@@ -915,7 +913,7 @@ State: 2 {0}
 [!1] 2
 --END--
 HOA: v1
-States: 4
+States: 3
 Start: 0
 AP: 2 "a" "b"
 acc-name: Buchi
@@ -927,16 +925,13 @@ State: 0
 [0] 1 {0}
 [!0] 2 {0}
 State: 1
-[1] 0
-[0&1] 1
+[1] 0 {0}
+[0&1] 1 {0}
 [!0&1] 2 {0}
 State: 2
 [!1] 0
-[0&!1] 1
-[!0&!1] 2
-[!0&!1] 3
-State: 3
-[!0&!1] 3 {0}
+[0&!1] 1 {0}
+[!0&!1] 2 {0}
 --END--
 HOA: v1
 States: 3
diff --git a/tests/python/automata.ipynb b/tests/python/automata.ipynb
index 07eda5fcb..09ecfe0be 100644
--- a/tests/python/automata.ipynb
+++ b/tests/python/automata.ipynb
@@ -30,155 +30,155 @@
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+       "<polygon fill=\"black\" stroke=\"black\" points=\"37.94,-22 30.94,-25.15 34.44,-22 30.94,-22 30.94,-22 30.94,-22 34.44,-22 30.94,-18.85 37.94,-22 37.94,-22\"/>\n",
        "</g>\n",
        "<!-- 0&#45;&gt;0 -->\n",
        "<g id=\"edge2\" class=\"edge\">\n",
        "<title>0&#45;&gt;0</title>\n",
-       "<path fill=\"none\" stroke=\"#000000\" d=\"M49.6208,-39.0373C48.3189,-48.8579 50.4453,-58 56,-58 60.166,-58 62.4036,-52.8576 62.7128,-46.1433\"/>\n",
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-       "<text text-anchor=\"start\" x=\"51.5\" y=\"-61.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">b</text>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M49.62,-39.04C48.32,-48.86 50.45,-58 56,-58 60.17,-58 62.4,-52.86 62.71,-46.14\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"62.38,-39.04 65.85,-45.88 62.54,-42.53 62.71,-46.03 62.71,-46.03 62.71,-46.03 62.54,-42.53 59.56,-46.18 62.38,-39.04 62.38,-39.04\"/>\n",
+       "<text text-anchor=\"start\" x=\"52\" y=\"-61.8\" font-family=\"Lato\" font-size=\"14.00\">b</text>\n",
        "</g>\n",
        "<!-- 1 -->\n",
        "<g id=\"node3\" class=\"node\">\n",
        "<title>1</title>\n",
-       "<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"190\" cy=\"-22\" rx=\"18\" ry=\"18\"/>\n",
-       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"190\" cy=\"-22\" rx=\"22\" ry=\"22\"/>\n",
-       "<text text-anchor=\"middle\" x=\"190\" y=\"-18.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1</text>\n",
+       "<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"188\" cy=\"-22\" rx=\"18\" ry=\"18\"/>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"188\" cy=\"-22\" rx=\"22\" ry=\"22\"/>\n",
+       "<text text-anchor=\"middle\" x=\"188\" y=\"-18.3\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
        "</g>\n",
        "<!-- 0&#45;&gt;1 -->\n",
        "<g id=\"edge3\" class=\"edge\">\n",
        "<title>0&#45;&gt;1</title>\n",
-       "<path fill=\"none\" stroke=\"#000000\" d=\"M74.0718,-22C96.2734,-22 134.2354,-22 160.6448,-22\"/>\n",
-       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"167.7645,-22 160.7646,-25.1501 164.2645,-22 160.7645,-22.0001 160.7645,-22.0001 160.7645,-22.0001 164.2645,-22 160.7645,-18.8501 167.7645,-22 167.7645,-22\"/>\n",
-       "<text text-anchor=\"start\" x=\"92\" y=\"-25.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a &amp; b &amp; c</text>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M74.26,-22C95.76,-22 132.79,-22 158.52,-22\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"165.78,-22 158.78,-25.15 162.28,-22 158.78,-22 158.78,-22 158.78,-22 162.28,-22 158.78,-18.85 165.78,-22 165.78,-22\"/>\n",
+       "<text text-anchor=\"start\" x=\"92\" y=\"-25.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; c</text>\n",
        "</g>\n",
        "<!-- 1&#45;&gt;1 -->\n",
        "<g id=\"edge4\" class=\"edge\">\n",
        "<title>1&#45;&gt;1</title>\n",
-       "<path fill=\"none\" stroke=\"#000000\" d=\"M178.0469,-40.5156C175.3906,-51.5833 179.375,-62 190,-62 198.3008,-62 202.5484,-55.6422 202.743,-47.5831\"/>\n",
-       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"201.9531,-40.5156 205.8612,-47.1224 202.3419,-43.994 202.7307,-47.4723 202.7307,-47.4723 202.7307,-47.4723 202.3419,-43.994 199.6002,-47.8222 201.9531,-40.5156 201.9531,-40.5156\"/>\n",
-       "<text text-anchor=\"start\" x=\"173\" y=\"-65.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a &amp; b</text>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M176.05,-40.52C173.39,-51.58 177.38,-62 188,-62 196.3,-62 200.55,-55.64 200.74,-47.58\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"199.95,-40.52 203.86,-47.12 200.34,-43.99 200.73,-47.47 200.73,-47.47 200.73,-47.47 200.34,-43.99 197.6,-47.82 199.95,-40.52 199.95,-40.52\"/>\n",
+       "<text text-anchor=\"start\" x=\"172\" y=\"-65.8\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b</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 0x7f8344049990> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fc93825d6c0> >"
       ]
      },
      "execution_count": 29,
@@ -3460,7 +3768,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.3"
+   "version": "3.8.2"
   }
  },
  "nbformat": 4,
diff --git a/tests/python/merge.py b/tests/python/merge.py
index a33a2774f..7fa888859 100644
--- a/tests/python/merge.py
+++ b/tests/python/merge.py
@@ -1,6 +1,6 @@
 #!/usr/bin/python3
 # -*- mode: python; coding: utf-8 -*-
-# Copyright (C) 2017 Laboratoire de Recherche et Développement de
+# Copyright (C) 2017, 2020 Laboratoire de Recherche et Développement de
 # l'EPITA.
 #
 # This file is part of Spot, a model checking library.
@@ -78,8 +78,7 @@ assert hoa == """HOA: v1
 States: 3
 Start: 0
 AP: 2 "a" "b"
-acc-name: parity min even 2
-Acceptance: 2 Inf(0) | Fin(1)
+Acceptance: 2 Fin(1) | Inf(0)
 properties: trans-labels explicit-labels trans-acc
 --BODY--
 State: 0
diff --git a/tests/python/simplacc.py b/tests/python/simplacc.py
index af8cb9298..024bccd56 100644
--- a/tests/python/simplacc.py
+++ b/tests/python/simplacc.py
@@ -57,23 +57,28 @@ for a in auts:
     b = spot.simplify_acceptance(a)
     assert b.equivalent_to(a)
     res.append(str(b.get_acceptance()))
+    c = spot.simplify_acceptance(b)
+    assert b.get_acceptance() == c.get_acceptance()
 
     a.set_acceptance(a.num_sets(), a.get_acceptance().complement())
     b = spot.simplify_acceptance(a)
     assert b.equivalent_to(a)
     res.append(str(b.get_acceptance()))
+    c = spot.simplify_acceptance(b)
+    assert b.get_acceptance() == c.get_acceptance()
+
 
 assert res == [
    'Inf(0)',
    'Fin(0)',
-   'Inf(1) & Fin(0)',
+   'Fin(0) & Inf(1)',
    'Fin(1) | Inf(0)',
-   'Inf(1) & (Fin(0) | Inf(2))',
+   '(Fin(0) | Inf(2)) & Inf(1)',
    'Fin(1) | (Fin(2) & Inf(0))',
    '(Fin(1) | Inf(2)) & Inf(0)',
    'Fin(0) | (Fin(2) & Inf(1))',
    '((Fin(1) | Inf(2)) & Inf(5)) | (Fin(0) & (Fin(1) | (Fin(3) & Inf(4))))',
    '(Fin(5) | (Fin(2) & Inf(1))) & (Inf(0) | ((Fin(4) | Inf(3)) & Inf(1)))',
-   'Inf(1) | Inf(0)',
-   'Fin(1) & Fin(0)',
+   'Inf(0)',
+   'Fin(0)',
    ]
diff --git a/tests/python/toparity.py b/tests/python/toparity.py
index 8301789b3..9ebaabc14 100644
--- a/tests/python/toparity.py
+++ b/tests/python/toparity.py
@@ -288,7 +288,7 @@ State: 4
 [0&!1] 4
 [0&1] 4 {1 2 4}
 --END--
-"""), [9, 6, 7, 7, 6, 6, 6])
+"""), [9, 6, 6, 6, 7, 6, 6])
 
 test(spot.automaton("""
 HOA: v1