diff --git a/spot/twaalgos/synthesis.cc b/spot/twaalgos/synthesis.cc
index 2143408b1..27e53b4d8 100644
--- a/spot/twaalgos/synthesis.cc
+++ b/spot/twaalgos/synthesis.cc
@@ -1006,8 +1006,10 @@ namespace spot
   }
 
   twa_graph_ptr
-  solved_game_to_separated_mealy(twa_graph_ptr arena, synthesis_info& gi)
+  solved_game_to_mealy(twa_graph_ptr arena, synthesis_info& gi)
   {
+    // This currently always produces either separated or split mealy machines
+    // if this changes, change also the other functions accordingly
     assert(arena->get_named_prop<region_t>("state-player")
            && "Need prop \"state-player\"");
     if (!arena)
@@ -1032,9 +1034,6 @@ namespace spot
     else if (gi.minimize_lvl >= 3)
       m = minimize_mealy(m, gi.minimize_lvl - 4);
 
-    if (!do_unsplit)
-      m = unsplit_mealy(m);
-
     if (gi.bv)
       {
         gi.bv->strat2aut_time += sw.stop();
@@ -1042,6 +1041,24 @@ namespace spot
         gi.bv->nb_strat_edges += m->num_edges();
       }
 
+    assert(is_mealy(m));
+    return m;
+  }
+
+  twa_graph_ptr
+  solved_game_to_mealy(twa_graph_ptr arena)
+  {
+    synthesis_info dummy;
+    return solved_game_to_mealy(arena, dummy);
+  }
+
+  twa_graph_ptr
+  solved_game_to_separated_mealy(twa_graph_ptr arena, synthesis_info& gi)
+  {
+    auto m = solved_game_to_mealy(arena, gi);
+
+    if (m->get_named_prop<region_t>("state-player"))
+      m = unsplit_mealy(m);
     assert(is_separated_mealy(m));
     return m;
   }
@@ -1053,6 +1070,27 @@ namespace spot
     return solved_game_to_separated_mealy(arena, dummy);
   }
 
+  twa_graph_ptr
+  solved_game_to_split_mealy(twa_graph_ptr arena, synthesis_info& gi)
+  {
+    auto m = solved_game_to_mealy(arena, gi);
+
+    if (!m->get_named_prop<region_t>("state-player"))
+      {
+        assert(is_separated_mealy(m));
+        split_separated_mealy_here(m);
+      }
+    assert(is_split_mealy(m));
+    return m;
+  }
+
+  twa_graph_ptr
+  solved_game_to_split_mealy(twa_graph_ptr arena)
+  {
+    synthesis_info dummy;
+    return solved_game_to_split_mealy(arena, dummy);
+  }
+
 }
 
 namespace spot
diff --git a/spot/twaalgos/synthesis.hh b/spot/twaalgos/synthesis.hh
index 9ecd90e73..44e6ca7dc 100644
--- a/spot/twaalgos/synthesis.hh
+++ b/spot/twaalgos/synthesis.hh
@@ -158,15 +158,25 @@ namespace spot
   /// @}
 
   /// \ingroup synthesis
-  /// \brief creates a separated mealy machine from a solved game
+  /// \brief creates a mealy machine from a solved game \a arena
   /// taking into account the options given in \a gi.
   /// This concerns in particular whether or not the machine is to be reduced
   /// and how.
+  /// solved_game_to_mealy can return any type of mealy machine. In fact it
+  /// will return the type that necessitates no additional operations
   /// @{
   SPOT_API twa_graph_ptr
+  solved_game_to_mealy(twa_graph_ptr arena, synthesis_info& gi);
+  SPOT_API twa_graph_ptr
+  solved_game_to_mealy(twa_graph_ptr arena);
+  SPOT_API twa_graph_ptr
   solved_game_to_separated_mealy(twa_graph_ptr arena, synthesis_info& gi);
   SPOT_API twa_graph_ptr
   solved_game_to_separated_mealy(twa_graph_ptr arena);
+  SPOT_API twa_graph_ptr
+  solved_game_to_split_mealy(twa_graph_ptr arena, synthesis_info& gi);
+  SPOT_API twa_graph_ptr
+  solved_game_to_split_mealy(twa_graph_ptr arena);
   /// @}
 
   /// \ingroup synthesis
diff --git a/tests/Makefile.am b/tests/Makefile.am
index febb2184b..60858d9c3 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -448,6 +448,7 @@ TESTS_python = \
   python/rs_like.py \
   python/sum.py \
   python/synthesis.py \
+  python/_synthesis.ipynb \
   python/toparity.py \
   python/trival.py \
   python/tra2tba.py \
diff --git a/tests/python/_synthesis.ipynb b/tests/python/_synthesis.ipynb
new file mode 100644
index 000000000..ee7cd9c1f
--- /dev/null
+++ b/tests/python/_synthesis.ipynb
@@ -0,0 +1,415 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import spot\n",
+    "spot.setup()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Additional testing for synthesis"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Testing the different methods to solve"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "si = spot.synthesis_info()\n",
+    "si.s = spot.synthesis_info.algo_LAR # Use LAR algorithm\n",
+    "game = spot.ltl_to_game(\"G((F(i0) && F(i1))->(G(i1<->(X(o0)))))\", [\"o0\"], si)\n",
+    "spot.solve_game(game)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "HOA: v1\n",
+      "States: 7\n",
+      "Start: 0\n",
+      "AP: 3 \"i1\" \"i0\" \"o0\"\n",
+      "acc-name: all\n",
+      "Acceptance: 0 t\n",
+      "properties: trans-labels explicit-labels state-acc deterministic\n",
+      "--BODY--\n",
+      "State: 0\n",
+      "[!0&!1] 1\n",
+      "[!0&1] 2\n",
+      "[0&!1] 3\n",
+      "[0&1] 4\n",
+      "State: 1\n",
+      "[0&1&!2] 4\n",
+      "[0&!1&!2] 3\n",
+      "[!0&1&!2] 2\n",
+      "[!0&!1&!2] 1\n",
+      "State: 2\n",
+      "[0&!2] 4\n",
+      "[!0&!2] 2\n",
+      "State: 3\n",
+      "[!0&1&2] 5\n",
+      "[0&1&2] 4\n",
+      "[!0&!1&2] 6\n",
+      "[0&!1&2] 3\n",
+      "State: 4\n",
+      "[!0&2] 5\n",
+      "[0&2] 4\n",
+      "State: 5\n",
+      "[!0&!2] 5\n",
+      "[0&!2] 4\n",
+      "State: 6\n",
+      "[!0&1&!2] 5\n",
+      "[0&1&!2] 4\n",
+      "[!0&!1&!2] 6\n",
+      "[0&!1&!2] 3\n",
+      "--END--\n",
+      "HOA: v1\n",
+      "States: 7\n",
+      "Start: 0\n",
+      "AP: 3 \"i1\" \"i0\" \"o0\"\n",
+      "acc-name: all\n",
+      "Acceptance: 0 t\n",
+      "properties: trans-labels explicit-labels state-acc deterministic\n",
+      "--BODY--\n",
+      "State: 0\n",
+      "[!0&!1] 1\n",
+      "[!0&1] 2\n",
+      "[0&!1] 3\n",
+      "[0&1] 4\n",
+      "State: 1\n",
+      "[0&1&!2] 4\n",
+      "[0&!1&!2] 3\n",
+      "[!0&1&!2] 2\n",
+      "[!0&!1&!2] 1\n",
+      "State: 2\n",
+      "[0&!2] 4\n",
+      "[!0&!2] 2\n",
+      "State: 3\n",
+      "[!0&1&2] 5\n",
+      "[0&1&2] 4\n",
+      "[!0&!1&2] 6\n",
+      "[0&!1&2] 3\n",
+      "State: 4\n",
+      "[!0&2] 5\n",
+      "[0&2] 4\n",
+      "State: 5\n",
+      "[!0&!2] 5\n",
+      "[0&!2] 4\n",
+      "State: 6\n",
+      "[!0&1&!2] 5\n",
+      "[0&1&!2] 4\n",
+      "[!0&!1&!2] 6\n",
+      "[0&!1&!2] 3\n",
+      "--END--\n",
+      "HOA: v1\n",
+      "States: 21\n",
+      "Start: 0\n",
+      "AP: 3 \"i1\" \"i0\" \"o0\"\n",
+      "acc-name: all\n",
+      "Acceptance: 0 t\n",
+      "properties: trans-labels explicit-labels state-acc deterministic\n",
+      "spot-state-player: 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
+      "--BODY--\n",
+      "State: 0\n",
+      "[!0&!1] 7\n",
+      "[!0&1] 8\n",
+      "[0&!1] 9\n",
+      "[0&1] 10\n",
+      "State: 1\n",
+      "[0&1] 11\n",
+      "[0&!1] 12\n",
+      "[!0&1] 13\n",
+      "[!0&!1] 14\n",
+      "State: 2\n",
+      "[0] 11\n",
+      "[!0] 13\n",
+      "State: 3\n",
+      "[!0&1] 15\n",
+      "[0&1] 16\n",
+      "[!0&!1] 17\n",
+      "[0&!1] 18\n",
+      "State: 4\n",
+      "[!0] 15\n",
+      "[0] 16\n",
+      "State: 5\n",
+      "[!0] 19\n",
+      "[0] 11\n",
+      "State: 6\n",
+      "[!0&1] 19\n",
+      "[0&1] 11\n",
+      "[!0&!1] 20\n",
+      "[0&!1] 12\n",
+      "State: 7\n",
+      "[t] 1\n",
+      "State: 8\n",
+      "[t] 2\n",
+      "State: 9\n",
+      "[t] 3\n",
+      "State: 10\n",
+      "[t] 4\n",
+      "State: 11\n",
+      "[!2] 4\n",
+      "State: 12\n",
+      "[!2] 3\n",
+      "State: 13\n",
+      "[!2] 2\n",
+      "State: 14\n",
+      "[!2] 1\n",
+      "State: 15\n",
+      "[2] 5\n",
+      "State: 16\n",
+      "[2] 4\n",
+      "State: 17\n",
+      "[2] 6\n",
+      "State: 18\n",
+      "[2] 3\n",
+      "State: 19\n",
+      "[!2] 5\n",
+      "State: 20\n",
+      "[!2] 6\n",
+      "--END--\n",
+      "HOA: v1\n",
+      "States: 2\n",
+      "Start: 1\n",
+      "AP: 3 \"i1\" \"i0\" \"o0\"\n",
+      "acc-name: all\n",
+      "Acceptance: 0 t\n",
+      "properties: trans-labels explicit-labels state-acc deterministic\n",
+      "--BODY--\n",
+      "State: 0\n",
+      "[0&1&!2] 1\n",
+      "[0&!1&!2] 1\n",
+      "[!0&1&!2] 0\n",
+      "[!0&!1&!2] 0\n",
+      "State: 1\n",
+      "[!0&1&2] 0\n",
+      "[0&1&2] 1\n",
+      "[!0&!1&2] 0\n",
+      "[0&!1&2] 1\n",
+      "--END--\n",
+      "HOA: v1\n",
+      "States: 2\n",
+      "Start: 1\n",
+      "AP: 3 \"i1\" \"i0\" \"o0\"\n",
+      "acc-name: all\n",
+      "Acceptance: 0 t\n",
+      "properties: trans-labels explicit-labels state-acc deterministic\n",
+      "--BODY--\n",
+      "State: 0\n",
+      "[0&1&!2] 1\n",
+      "[0&!1&!2] 1\n",
+      "[!0&1&!2] 0\n",
+      "[!0&!1&!2] 0\n",
+      "State: 1\n",
+      "[!0&1&2] 0\n",
+      "[0&1&2] 1\n",
+      "[!0&!1&2] 0\n",
+      "[0&!1&2] 1\n",
+      "--END--\n",
+      "HOA: v1\n",
+      "States: 6\n",
+      "Start: 1\n",
+      "AP: 3 \"i1\" \"i0\" \"o0\"\n",
+      "acc-name: all\n",
+      "Acceptance: 0 t\n",
+      "properties: trans-labels explicit-labels state-acc deterministic\n",
+      "spot-state-player: 0 0 1 1 1 1\n",
+      "--BODY--\n",
+      "State: 0\n",
+      "[0&1] 2\n",
+      "[0&!1] 2\n",
+      "[!0&1] 3\n",
+      "[!0&!1] 3\n",
+      "State: 1\n",
+      "[!0&1] 4\n",
+      "[0&1] 5\n",
+      "[!0&!1] 4\n",
+      "[0&!1] 5\n",
+      "State: 2\n",
+      "[!2] 1\n",
+      "State: 3\n",
+      "[!2] 0\n",
+      "State: 4\n",
+      "[2] 0\n",
+      "State: 5\n",
+      "[2] 1\n",
+      "--END--\n",
+      "HOA: v1\n",
+      "States: 6\n",
+      "Start: 1\n",
+      "AP: 3 \"i1\" \"i0\" \"o0\"\n",
+      "acc-name: all\n",
+      "Acceptance: 0 t\n",
+      "properties: trans-labels explicit-labels state-acc deterministic\n",
+      "spot-state-player: 0 0 1 1 1 1\n",
+      "--BODY--\n",
+      "State: 0\n",
+      "[0] 3\n",
+      "[!0] 4\n",
+      "State: 1\n",
+      "[0] 2\n",
+      "[!0] 5\n",
+      "State: 2\n",
+      "[2] 1\n",
+      "State: 3\n",
+      "[!2] 1\n",
+      "State: 4\n",
+      "[!2] 0\n",
+      "State: 5\n",
+      "[2] 0\n",
+      "--END--\n",
+      "HOA: v1\n",
+      "States: 2\n",
+      "Start: 0\n",
+      "AP: 3 \"i1\" \"i0\" \"o0\"\n",
+      "acc-name: all\n",
+      "Acceptance: 0 t\n",
+      "properties: trans-labels explicit-labels state-acc deterministic\n",
+      "--BODY--\n",
+      "State: 0\n",
+      "[0&2] 0\n",
+      "[!0&2] 1\n",
+      "State: 1\n",
+      "[0&!2] 0\n",
+      "[!0&!2] 1\n",
+      "--END--\n",
+      "HOA: v1\n",
+      "States: 6\n",
+      "Start: 1\n",
+      "AP: 3 \"i1\" \"i0\" \"o0\"\n",
+      "acc-name: all\n",
+      "Acceptance: 0 t\n",
+      "properties: trans-labels explicit-labels state-acc deterministic\n",
+      "spot-state-player: 0 0 1 1 1 1\n",
+      "--BODY--\n",
+      "State: 0\n",
+      "[0] 3\n",
+      "[!0] 4\n",
+      "State: 1\n",
+      "[0] 2\n",
+      "[!0] 5\n",
+      "State: 2\n",
+      "[2] 1\n",
+      "State: 3\n",
+      "[!2] 1\n",
+      "State: 4\n",
+      "[!2] 0\n",
+      "State: 5\n",
+      "[2] 0\n",
+      "--END--\n"
+     ]
+    }
+   ],
+   "source": [
+    "si.minimize_lvl = 0\n",
+    "mm0 = spot.solved_game_to_mealy(game, si)\n",
+    "msep0 = spot.solved_game_to_separated_mealy(game, si)\n",
+    "msplit0 = spot.solved_game_to_split_mealy(game, si)\n",
+    "assert(spot.is_separated_mealy(mm0)) #Not imposed by the functions pre or post, but results of current impl, change if necessary\n",
+    "assert(spot.is_separated_mealy(msep0))\n",
+    "assert(spot.is_split_mealy(msplit0))\n",
+    "print(mm0.to_str(\"hoa\"))\n",
+    "print(msep0.to_str(\"hoa\"))\n",
+    "print(msplit0.to_str(\"hoa\"))\n",
+    "si.minimize_lvl = 2\n",
+    "mm2 = spot.solved_game_to_mealy(game, si)\n",
+    "msep2 = spot.solved_game_to_separated_mealy(game, si)\n",
+    "msplit2 = spot.solved_game_to_split_mealy(game, si)\n",
+    "assert(spot.is_separated_mealy(mm2)) #Not imposed by the functions pre or post, but results of current impl, change if necessary\n",
+    "assert(spot.is_separated_mealy(msep2))\n",
+    "assert(spot.is_split_mealy(msplit2))\n",
+    "print(mm2.to_str(\"hoa\"))\n",
+    "print(msep2.to_str(\"hoa\"))\n",
+    "print(msplit2.to_str(\"hoa\"))\n",
+    "si.minimize_lvl = 3\n",
+    "mm3 = spot.solved_game_to_mealy(game, si)\n",
+    "msep3 = spot.solved_game_to_separated_mealy(game, si)\n",
+    "msplit3 = spot.solved_game_to_split_mealy(game, si)\n",
+    "assert(spot.is_split_mealy(mm3)) #Not imposed by the functions pre or post, but results of current impl, change if necessary\n",
+    "assert(spot.is_separated_mealy(msep3))\n",
+    "assert(spot.is_split_mealy(msplit3))\n",
+    "print(mm3.to_str(\"hoa\"))\n",
+    "print(msep3.to_str(\"hoa\"))\n",
+    "print(msplit3.to_str(\"hoa\"))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "mus0 = spot.unsplit_mealy(msplit0)\n",
+    "mus2 = spot.unsplit_mealy(msplit2)\n",
+    "mus3 = spot.unsplit_mealy(msplit3)\n",
+    "mmus3 = spot.unsplit_mealy(mm3)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "assert(mm0.equivalent_to(msep0))\n",
+    "assert(mm0.equivalent_to(mus0))\n",
+    "assert(mm2.equivalent_to(msep2))\n",
+    "assert(mm2.equivalent_to(mus2))\n",
+    "assert(mmus3.equivalent_to(msep3))\n",
+    "assert(mmus3.equivalent_to(mus3))"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.10"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}