diff --git a/spot/twaalgos/toparity.cc b/spot/twaalgos/toparity.cc
index 056daaf40..32f5c7570 100644
--- a/spot/twaalgos/toparity.cc
+++ b/spot/twaalgos/toparity.cc
@@ -1684,7 +1684,7 @@ run()
         res_->set_named_prop("state-names", names);
     reduce_parity_here(res_);
     res_->purge_unreachable_states();
-    res_->merge_states();
+    // res_->merge_states();
     return res_;
 }
 
diff --git a/tests/python/automata.ipynb b/tests/python/automata.ipynb
index 61971c52e..07eda5fcb 100644
--- a/tests/python/automata.ipynb
+++ b/tests/python/automata.ipynb
@@ -30,155 +30,155 @@
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       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fa0442e1e40> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f8344049990> >"
       ]
      },
      "execution_count": 29,
@@ -3614,7 +3460,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.2"
+   "version": "3.7.3"
   }
  },
  "nbformat": 4,
diff --git a/tests/python/toparity.py b/tests/python/toparity.py
index 237dacb05..91732922e 100644
--- a/tests/python/toparity.py
+++ b/tests/python/toparity.py
@@ -195,7 +195,7 @@ State: 13
 [0&1] 5
 [!0&!1] 10 {0 1 3 5}
 [0&!1] 13 {1 3}
---END--"""), [31, 27, 23, 28, 28, 24, 22])
+--END--"""), [35, 30, 23, 30, 34, 27, 22])
 
 test(spot.automaton("""
 HOA: v1
@@ -213,7 +213,7 @@ State: 1
 [0&!1] 1 {4}
 [!0&1] 1 {0 1 2 3}
 [!0&!1] 1 {0 3}
---END--"""), [7, 5, 3, 6, 5, 5, 3])
+--END--"""), [7, 7, 3, 6, 10, 5, 3])
 
 
 for i,f in enumerate(spot.randltl(10, 400)):
@@ -288,7 +288,7 @@ State: 4
 [0&!1] 4
 [0&1] 4 {1 2 4}
 --END--
-"""), [8, 6, 7, 7, 6, 6, 6])
+"""), [9, 9, 8, 7, 9, 9, 6])
 
 test(spot.automaton("""
 HOA: v1
@@ -310,7 +310,7 @@ State: 1
 [0&!1] 1 {2 3}
 [0&1] 1 {1 2 4}
 --END--
-"""), [11, 6, 3, 7, 7, 4, 3])
+"""), [11, 6, 4, 7, 11, 6, 3])
 
 
 # Tests both the old and new version of to_parity
@@ -341,7 +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, [6, 6, 6, 6, 6, 6, 6])
+test(a, [8, 7, 8, 8, 8, 7, 6])
 
 # Force a few edges to false, to make sure to_parity() is OK with that.
 for e in a.out(2):
@@ -355,7 +355,7 @@ for e in a.out(3):
 p = spot.to_parity_old(a, True)
 assert p.num_states() == 22
 assert spot.are_equivalent(a, p)
-test(a, [7, 6, 7, 7, 6, 6, 6])
+test(a, [7, 6, 7, 7, 7, 6, 6])
 
 for f in spot.randltl(4, 400):
     d = spot.translate(f, "det", "G")
@@ -371,4 +371,4 @@ 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, [6, 6, 3, 6, 7, 6, 3])
+test(a, [7, 7, 3, 7, 8, 7, 3])