diff --git a/spot/twa/acc.hh b/spot/twa/acc.hh
index 1d7e68a3d..6c17d073f 100644
--- a/spot/twa/acc.hh
+++ b/spot/twa/acc.hh
@@ -471,7 +471,8 @@ namespace spot
     {
       private:
       bool
-      get_alone_mark(bool& fin, acc_cond::mark_t& mark, bool& conj, acc_code& code)
+      get_alone_mark(bool& fin, acc_cond::mark_t& mark, bool& conj,
+                      acc_code& code)
       {
         auto elements = top_conjuncts();
         conj = (elements.size() > 1);
@@ -510,19 +511,25 @@ namespace spot
           auto elements = result.top_disjuncts();
           if (elements.size() < 2)
             elements = result.top_conjuncts();
-          result = std::accumulate(elements.begin(), elements.end(), code,
+          acc_code init_code;
+          if (conj)
+            init_code = acc_code::t();
+          else
+            init_code = acc_code::f();
+          bool keeped_code = false;
+          result = std::accumulate(elements.rbegin(), elements.rend(),
+          init_code,
             [&](acc_code a, acc_code b)
             {
-              if (b != code)
-              {
-                b = b.remove(mark, !fin);
-                if (conj)
-                  return a & b;
-                else
-                  return a | b;
-              }
-              return a;
-            });
+              if (b != code || keeped_code)
+                b = b.remove(mark, fin == conj);
+              if (b == code)
+                keeped_code = true;
+              if (conj)
+                return a & b;
+              else
+                return a | b;
+              });
         }
         std::vector<acc_code> elements = result.top_disjuncts();
         if (elements.size() < 2)
@@ -534,7 +541,8 @@ namespace spot
             init_code = acc_code::t();
           else
             init_code = acc_code::f();
-          result = std::accumulate(elements.begin(), elements.end(), init_code,
+          result = std::accumulate(elements.rbegin(), elements.rend(),
+          init_code,
             [&](acc_code a, acc_code b)
             {
                 if (conj)
diff --git a/spot/twaalgos/cleanacc.cc b/spot/twaalgos/cleanacc.cc
index 8065cc8f6..8a3772c8b 100644
--- a/spot/twaalgos/cleanacc.cc
+++ b/spot/twaalgos/cleanacc.cc
@@ -619,8 +619,13 @@ namespace spot
         simplify_complementary_marks_here(aut);
         fuse_marks_here(aut);
       }
-    aut->set_acceptance(aut->acc().propagate_fin_inf());
     cleanup_acceptance_here(aut, true);
+    auto prop_cond = aut->acc().propagate_fin_inf();
+    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 1feb8fed4..2339690bc 100755
--- a/tests/core/accsimpl.test
+++ b/tests/core/accsimpl.test
@@ -49,5 +49,5 @@ State: 0
 EOF
 
 autfilt --simplify-acceptance 325 > 325s
-exp='4 Fin(0) | (Fin(0) & Inf(1)) | (Fin(2) & Inf(3))'
+exp='3 Fin(0) | (Fin(1) & Inf(2))'
 test "$exp" = "`autfilt --stats='%a %g' 325s`"
diff --git a/tests/core/remfin.test b/tests/core/remfin.test
index c50272339..0b387d8e0 100755
--- a/tests/core/remfin.test
+++ b/tests/core/remfin.test
@@ -336,27 +336,24 @@ State: 3
 [!0&!1] 3 {0}
 --END--
 HOA: v1
-States: 4
+States: 3
 Start: 0
 AP: 2 "a" "b"
-Acceptance: 4 (Inf(0)&Inf(1)) | Inf(0) | (Inf(2)&Inf(3))
+Acceptance: 3 (Inf(1)&Inf(2)) | Inf(0)
 properties: trans-labels explicit-labels trans-acc
 --BODY--
 State: 0
-[t] 0 {3}
-[0] 1 {3}
-[!0] 2 {0 3}
+[t] 0 {2}
+[0] 1 {2}
+[!0] 2 {0 2}
 State: 1
-[1] 0 {3}
-[0&1] 1 {0 3}
-[!0&1] 2 {2 3}
+[1] 0 {2}
+[0&1] 1 {0 2}
+[!0&1] 2 {1 2}
 State: 2
 [!1] 0
 [0&!1] 1 {0}
 [!0&!1] 2 {0}
-[!0&!1] 3
-State: 3
-[!0&!1] 3 {0 1}
 --END--
 HOA: v1
 States: 1
@@ -942,7 +939,7 @@ State: 3
 [!0&!1] 3 {0}
 --END--
 HOA: v1
-States: 4
+States: 3
 Start: 0
 AP: 2 "a" "b"
 acc-name: Buchi
@@ -961,9 +958,6 @@ State: 2
 [!1] 0
 [0&!1] 1 {0}
 [!0&!1] 2 {0}
-[!0&!1] 3
-State: 3
-[!0&!1] 3 {0}
 --END--
 HOA: v1
 States: 1
diff --git a/tests/python/automata.ipynb b/tests/python/automata.ipynb
index 56472b1f5..61971c52e 100644
--- a/tests/python/automata.ipynb
+++ b/tests/python/automata.ipynb
@@ -33,11 +33,11 @@
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        "<g id=\"edge3\" class=\"edge\">\n",
        "<title>0&#45;&gt;1</title>\n",
-       "<path fill=\"none\" stroke=\"black\" d=\"M74.26,-22C96.23,-22 134.49,-22 160.75,-22\"/>\n",
-       "<polygon fill=\"black\" stroke=\"black\" points=\"167.81,-22 160.81,-25.15 164.31,-22 160.81,-22 160.81,-22 160.81,-22 164.31,-22 160.81,-18.85 167.81,-22 167.81,-22\"/>\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=\"black\" d=\"M178.05,-40.52C175.39,-51.58 179.38,-62 190,-62 198.3,-62 202.55,-55.64 202.74,-47.58\"/>\n",
-       "<polygon fill=\"black\" stroke=\"black\" points=\"201.95,-40.52 205.86,-47.12 202.34,-43.99 202.73,-47.47 202.73,-47.47 202.73,-47.47 202.34,-43.99 199.6,-47.82 201.95,-40.52 201.95,-40.52\"/>\n",
-       "<text text-anchor=\"start\" x=\"173\" y=\"-65.8\" font-family=\"Lato\" font-size=\"14.00\">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 0x7fde006412d0> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fa0442e1e40> >"
       ]
      },
      "execution_count": 29,
@@ -3734,7 +3614,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.5"
+   "version": "3.8.2"
   }
  },
  "nbformat": 4,
diff --git a/tests/python/merge.py b/tests/python/merge.py
index 5d0997a25..161b9b6fd 100644
--- a/tests/python/merge.py
+++ b/tests/python/merge.py
@@ -78,7 +78,7 @@ assert hoa == """HOA: v1
 States: 3
 Start: 0
 AP: 2 "a" "b"
-Acceptance: 2 Fin(1) | (Inf(0)&Inf(1))
+Acceptance: 2 Fin(1) | Inf(0)
 properties: trans-labels explicit-labels trans-acc
 --BODY--
 State: 0
diff --git a/tests/python/toparity.py b/tests/python/toparity.py
index d6159ae83..95c01ad61 100644
--- a/tests/python/toparity.py
+++ b/tests/python/toparity.py
@@ -19,6 +19,7 @@
 # along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
 import spot
+import itertools
 
 # Tests for the new version of to_parity
 
@@ -89,8 +90,9 @@ options = [
 ]
 
 
-def test(aut, full=True):
-    for opt in options:
+def test(aut, expected_num_states=[], full=True):
+    for (opt, expected_num) in\
+            itertools.zip_longest(options, expected_num_states):
         p1 = spot.to_parity(aut,
                             search_ex = opt.search_ex,
                             use_last = opt.use_last,
@@ -105,6 +107,8 @@ def test(aut, full=True):
                             pretty_print = opt.pretty_print,
                             )
         assert spot.are_equivalent(aut, p1)
+        if (expected_num != None):
+                assert(p1.num_states() == expected_num)
         if full:
             # Make sure passing opt is the same as setting
             # each argument individually
@@ -191,7 +195,7 @@ State: 13
 [0&1] 5
 [!0&!1] 10 {0 1 3 5}
 [0&!1] 13 {1 3}
---END--"""))
+--END--"""), [35, 28, 23, 30, 29, 25, 22])
 
 test(spot.automaton("""
 HOA: v1
@@ -209,7 +213,7 @@ State: 1
 [0&!1] 1 {4}
 [!0&1] 1 {0 1 2 3}
 [!0&!1] 1 {0 3}
---END--"""))
+--END--"""), [7, 5, 3, 6, 5, 5, 3])
 
 
 for i,f in enumerate(spot.randltl(10, 400)):
@@ -250,7 +254,7 @@ State: 3
 [!0&1] 2 {1 4}
 [0&1] 3 {0}
 --END--
-"""))
+"""), [80, 22, 80, 80, 80, 17, 10])
 
 test(spot.automaton("""
 HOA: v1
@@ -284,7 +288,7 @@ State: 4
 [0&!1] 4
 [0&1] 4 {1 2 4}
 --END--
-"""))
+"""), [9, 6, 6, 6, 7, 6, 6])
 
 test(spot.automaton("""
 HOA: v1
@@ -306,7 +310,7 @@ State: 1
 [0&!1] 1 {2 3}
 [0&1] 1 {1 2 4}
 --END--
-"""))
+"""), [11, 6, 3, 7, 7, 4, 3])
 
 
 # Tests both the old and new version of to_parity
@@ -337,8 +341,7 @@ explicit-labels trans-acc --BODY-- State: 0 [0&1] 2 {4 5} [0&1] 4 {0 4}
 p = spot.to_parity_old(a, True)
 assert p.num_states() == 22
 assert spot.are_equivalent(a, p)
-test(a)
-assert spot.to_parity(a).num_states() == 6
+test(a, [8, 7, 8, 8, 6, 7, 6])
 
 for f in spot.randltl(4, 400):
     d = spot.translate(f, "det", "G")
@@ -354,4 +357,4 @@ 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)
+test(a, [7, 7, 3, 7, 8, 7, 3])