diff --git a/spot/twaalgos/aiger.cc b/spot/twaalgos/aiger.cc
index efd0a13fc..6b52ee542 100644
--- a/spot/twaalgos/aiger.cc
+++ b/spot/twaalgos/aiger.cc
@@ -1401,7 +1401,9 @@ namespace
   static aig_ptr
   auts_to_aiger(const std::vector<std::pair<const_twa_graph_ptr, bdd>>&
                     strat_vec,
-                const char* mode)
+                const char* mode,
+                const std::vector<std::string>& unused_ins = {},
+                const std::vector<std::string>& unused_outs = {})
   {
     // The aiger circuit cannot encode the acceptance condition
     // Test that the acceptance condition is true
@@ -1459,6 +1461,17 @@ namespace
         }
     }
 
+    // Create two new vector holding used and unused inputs/outputs
+    // Used propositions appear first
+    std::vector<std::string> input_names_all = input_names;
+    input_names_all.insert(input_names_all.end(),
+                           unused_ins.cbegin(),
+                          unused_ins.cend());
+    std::vector<std::string> output_names_all = output_names;
+    output_names_all.insert(output_names_all.end(),
+                            unused_outs.cbegin(),
+                            unused_outs.cend());
+
     // Decide on which outcond to use
     // The edges of the automaton all have the form in&out
     // due to the unsplit
@@ -1530,7 +1543,7 @@ namespace
 
     assert(output_names.size() == (unsigned) bdd_nodecount(all_outputs));
     aig_ptr circuit_ptr =
-        std::make_shared<aig>(input_names, output_names,
+        std::make_shared<aig>(input_names_all, output_names_all,
                               n_latches, strat_vec[0].first->get_dict());
     aig& circuit = *circuit_ptr;
 
@@ -1770,6 +1783,10 @@ namespace
     // Reset them
     for (unsigned i = 0; i < n_outs; ++i)
       circuit.set_output(i, bdd2var_min(out[i], out_dc[i]));
+    // Add the unused propositions
+    const unsigned n_outs_all = output_names_all.size();
+    for (unsigned i = n_outs; i < n_outs_all; ++i)
+      circuit.set_output(i, circuit.aig_false());
     for (unsigned i = 0; i < n_latches; ++i)
       circuit.set_next_latch(i, bdd2var_min(latch[i], bddfalse));
     return circuit_ptr;
@@ -1832,15 +1849,26 @@ namespace spot
       check_double_names(all_ap, "Atomic propositions appears in input "
                                  "and output propositions; ");
     }
-    // Register all to make sure they exist in the aut
-    std::for_each(ins.begin(), ins.end(),
-                  [s = aut](auto&& e){s->register_ap(e); });
-    bdd all_outputs = bddtrue;
-    std::for_each(outs.begin(), outs.end(),
-                  [&ao = all_outputs, s=aut](auto&& e)
-                  {ao &= bdd_ithvar(s->register_ap(e)); });
+    // Check if there exist outs or ins that are not used by the
+    // strategy
+    // ins -> simply declare them
+    // outs -> set them to false
+    std::vector<std::string> unused_outs;
+    std::vector<std::string> unused_ins;
+    {
+      std::set<std::string> used_aps;
+      for (const auto& f : aut->ap())
+        used_aps.insert(f.ap_name());
+      for (const auto& ao : outs)
+        if (!used_aps.count(ao))
+          unused_outs.push_back(ao);
+      for (const auto& ai : ins)
+        if (!used_aps.count(ai))
+          unused_outs.push_back(ai);
+    }
     // todo Some additional checks?
-    return auts_to_aiger({{aut, all_outputs}}, mode);
+    return auts_to_aiger({{aut, get_synthesis_outputs(aut)}}, mode,
+                         unused_ins, unused_outs);
   }
 
   // Note: This ignores the named property
@@ -1875,22 +1903,32 @@ namespace spot
     std::vector<std::pair<const_twa_graph_ptr, bdd>> new_vec;
     new_vec.reserve(strat_vec.size());
 
+    std::set<std::string> used_aps;
+
     for (size_t i = 0; i < strat_vec.size(); ++i)
       {
-        // Register all to make sure they exist in the aut
-        std::for_each(ins.begin(), ins.end(),
-                      [s=strat_vec[i]](auto&& e){s->register_ap(e); });
-        bdd this_outputs = bddtrue;
-        std::for_each(outs[i].begin(), outs[i].end(),
-                      [&to = this_outputs, s=strat_vec[i]](auto&& e)
-                      {to &= bdd_ithvar(s->register_ap(e)); });
-        if (this_outputs == bddfalse)
-          throw std::runtime_error("Inconsistency in outputs of strat "
-                                   + std::to_string(i) + ".\n");
+        for (const auto& f : strat_vec[i]->ap())
+          used_aps.insert(f.ap_name());
         // todo Some additional checks?
-        new_vec.emplace_back(strat_vec[i], this_outputs);
+        new_vec.emplace_back(strat_vec[i],
+                             get_synthesis_outputs(strat_vec[i]));
       }
-    return auts_to_aiger(new_vec, mode);
+
+        // Check if there exist outs or ins that are not used by the
+    // strategy
+    // ins -> simply declare them
+    // outs -> set them to false
+    std::vector<std::string> unused_outs;
+    std::vector<std::string> unused_ins;
+    for (const auto& cao : outs)
+      for (const auto& ao : cao)
+        if (!used_aps.count(ao))
+          unused_outs.push_back(ao);
+    for (const auto& ai : ins)
+      if (!used_aps.count(ai))
+        unused_outs.push_back(ai);
+
+    return auts_to_aiger(new_vec, mode, unused_ins, unused_outs);
   }
 
   aig_ptr
diff --git a/spot/twaalgos/aiger.hh b/spot/twaalgos/aiger.hh
index 4f09f12a0..410e4ea08 100644
--- a/spot/twaalgos/aiger.hh
+++ b/spot/twaalgos/aiger.hh
@@ -437,6 +437,10 @@ namespace spot
   /// \note The states of each strategy are represented by a block of latches
   ///       not affected by the others. For this to work in a general setting,
   ///       the outputs must be disjoint.
+  /// \note Attention: Only the propositions actually used in the strategy
+  ///       appear in the aiger circuit. So it can happen that, for instance,
+  ///       propositions marked as output during the call to create_game
+  ///       are absent.
   SPOT_API aig_ptr
   strategies_to_aig(const std::vector<const_twa_graph_ptr>& strat_vec,
                     const char* mode);
@@ -444,12 +448,16 @@ namespace spot
   /// \brief Like above, but explicitly handing over which propositions
   ///        are inputs and outputs and does therefore not rely on the
   ///        named property "synthesis-outputs"
+  /// \note All properties in ins and out are guaranteed to appear in the
+  ///       aiger circuit.
   SPOT_API aig_ptr
   strategy_to_aig(const twa_graph_ptr& aut, const char *mode,
                   const std::vector<std::string>& ins,
                   const std::vector<std::string>& outs);
 
   /// \brief Like above, but explicitly handing over the propositions
+  /// \note All properties in ins and out are guaranteed to appear in the
+  ///       aiger circuit.
   SPOT_API aig_ptr
   strategies_to_aig(const std::vector<twa_graph_ptr>& strat_vec,
                     const char* mode,
diff --git a/tests/python/games.ipynb b/tests/python/games.ipynb
index 6b44b2343..09073f423 100644
--- a/tests/python/games.ipynb
+++ b/tests/python/games.ipynb
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+       "<text text-anchor=\"start\" x=\"208.1644\" y=\"-241.8543\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">b</text>\n",
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        "</g>\n",
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7e12721660> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7c803ddea0> >"
       ]
      },
      "execution_count": 15,
@@ -3784,13 +3784,6 @@
     "spot.highlight_strategy(game)"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -3828,8 +3821,7 @@
       "i0 a\n",
       "i1 b\n",
       "o0 c\n",
-      "o1 d\n",
-      "\n"
+      "o1 d\n"
      ]
     }
    ],
@@ -3846,8 +3838,7 @@
     "i0 a\n",
     "i1 b\n",
     "o0 c\n",
-    "o1 d\n",
-    "\"\"\"\n",
+    "o1 d\"\"\"\n",
     "print(aag_txt)"
    ]
   },
@@ -3871,103 +3862,102 @@
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@@ -4004,8 +3994,7 @@
       "i0 i0\n",
       "i1 i1\n",
       "o0 o0\n",
-      "o1 o1\n",
-      "\n"
+      "o1 o1\n"
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@@ -4052,40 +4041,40 @@
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-       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7e11cdd0f0> >"
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7f7c804061b0> >"
       ]
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      "metadata": {},
@@ -4098,16 +4087,300 @@
    ]
   },
   {
-   "cell_type": "code",
-   "execution_count": null,
+   "cell_type": "markdown",
    "metadata": {},
-   "outputs": [],
-   "source": []
+   "source": [
+    "<h2>Incomplete circuit</h2>\n",
+    "\n",
+    "<p>\n",
+    "    It can happen that propositions declared as output are ommited in the aig circuit.\n",
+    "    This happens if the output does not appear in the strategy. Since it does not appear in the\n",
+    "    strategy it can take arbritrary values.\n",
+    "</p>"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "True\n"
+     ]
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+       "<text text-anchor=\"start\" x=\"198.5\" y=\"-34.4845\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#6a3d9a\">❸</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 0x7f7c80406540> >"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "game = spot.create_game(\"o0\", [\"o0\", \"o1\"])\n",
+    "print(spot.solve_game(game))\n",
+    "spot.highlight_strategy(game)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [
+    {
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+       "<title>0&#45;&gt;L0</title>\n",
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+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<spot.aig; proxy of <Swig Object of type 'spot::aig_ptr *' at 0x7f7c803fa0c0> >"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "strat = spot.create_strategy(game)\n",
+    "aig = spot.strategy_to_aig(strat, \"isop\")\n",
+    "aig"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "By handing over the input and output propositions explicitly, you can force their appearance of the propositions in the circuit"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "metadata": {},
+   "outputs": [
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+       "<polygon fill=\"none\" stroke=\"#000000\" points=\"149.1961,-108 95.1961,-108 95.1961,-72 149.1961,-72 149.1961,-108\"/>\n",
+       "<text text-anchor=\"middle\" x=\"122.1961\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">L0</text>\n",
+       "</g>\n",
+       "<!-- 0 -->\n",
+       "<g id=\"node3\" class=\"node\">\n",
+       "<title>0</title>\n",
+       "<polygon fill=\"none\" stroke=\"#000000\" points=\"178.6961,-36 119.6961,-36 119.6961,0 178.6961,0 178.6961,-36\"/>\n",
+       "<text text-anchor=\"middle\" x=\"149.1961\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">Const</text>\n",
+       "</g>\n",
+       "<!-- 0&#45;&gt;L0 -->\n",
+       "<g id=\"edge1\" class=\"edge\">\n",
+       "<title>0&#45;&gt;L0</title>\n",
+       "<path fill=\"none\" stroke=\"#000000\" d=\"M142.3828,-36.1686C139.4317,-44.0383 135.9103,-53.4288 132.6411,-62.1467\"/>\n",
+       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"129.3352,-60.9945 129.1011,-71.5867 135.8895,-63.4524 129.3352,-60.9945\"/>\n",
+       "</g>\n",
+       "<!-- o1o1 -->\n",
+       "<g id=\"node5\" class=\"node\">\n",
+       "<title>o1o1</title>\n",
+       "<polygon fill=\"none\" stroke=\"#000000\" points=\"177.1961,-144 221.5891,-178.5 132.803,-178.5 177.1961,-144\"/>\n",
+       "<text text-anchor=\"middle\" x=\"177.1961\" y=\"-163.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">o1</text>\n",
+       "</g>\n",
+       "<!-- 0&#45;&gt;o1o1 -->\n",
+       "<g id=\"edge3\" class=\"edge\">\n",
+       "<title>0&#45;&gt;o1o1:s</title>\n",
+       "<path fill=\"none\" stroke=\"#000000\" d=\"M155.8317,-36.0824C163.4001,-58.2228 174.9827,-97.2894 176.9175,-133.7894\"/>\n",
+       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"173.4246,-134.0992 177.1961,-144 180.422,-133.9082 173.4246,-134.0992\"/>\n",
+       "</g>\n",
+       "</g>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<spot.aig; proxy of <Swig Object of type 'spot::aig_ptr *' at 0x7f7c803fa510> >"
+      ]
+     },
+     "execution_count": 24,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "aig2 = spot.strategy_to_aig(strat, \"isop\", [], [\"o0\", \"o1\"])\n",
+    "aig2"
+   ]
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3 (ipykernel)",
+   "display_name": "Python 3",
    "language": "python",
    "name": "python3"
   },
@@ -4121,7 +4394,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.10"
+   "version": "3.7.3"
   }
  },
  "nbformat": 4,