diff --git a/doc/org/concepts.org b/doc/org/concepts.org
index 440ec2126..db5bc157e 100644
--- a/doc/org/concepts.org
+++ b/doc/org/concepts.org
@@ -1128,7 +1128,7 @@ Here is a list of named properties currently used inside Spot:
 | ~highlight-edges~   | ~std::map<unsigned, unsigned>~ | map of (edge number, color number) for highlighting the output                                                                  |
 | ~highlight-states~  | ~std::map<unsigned, unsigned>~ | map of (state number, color number) for highlighting the output                                                                 |
 | ~incomplete-states~ | ~std::set<unsigned>~           | set of states numbers that should be displayed as incomplete  (used internally by ~print_dot()~ when truncating large automata) |
-| ~degen-levels~      | ~std::vector<unsigned>~        | level associated to each state by the degenaralization algorithm                                                                |
+| ~degen-levels~      | ~std::vector<unsigned>~        | level associated to each state by the degeneralization algorithm                                                                |
 | ~simulated-states~  | ~std::vector<unsigned>~        | map states of the original automaton to states if the current automaton in the result of simulation-based reductions            |
 
 Objects referenced via named properties are automatically destroyed
diff --git a/spot/twa/twagraph.cc b/spot/twa/twagraph.cc
index f69baa57c..bc8fd342a 100644
--- a/spot/twa/twagraph.cc
+++ b/spot/twa/twagraph.cc
@@ -620,6 +620,16 @@ namespace spot
           }
         dl->resize(used_states);
       }
+    if (auto ss = get_named_prop<std::vector<unsigned>>("simulated-states"))
+      {
+        for (auto& s : *ss)
+          {
+            if (s >= newst.size())
+              s = -1U;
+            else
+              s = newst[s];
+          }
+      }
     init_number_ = newst[init_number_];
     g_.defrag_states(std::move(newst), used_states);
   }
diff --git a/spot/twaalgos/simulation.hh b/spot/twaalgos/simulation.hh
index 07defa2e7..241b7fd15 100644
--- a/spot/twaalgos/simulation.hh
+++ b/spot/twaalgos/simulation.hh
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2012, 2013, 2014, 2015 Laboratoire de Recherche et
+// Copyright (C) 2012, 2013, 2014, 2015, 2017 Laboratoire de Recherche et
 // Développement de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
@@ -64,6 +64,12 @@ namespace spot
   /// acceptance conditions than necessary, and running scc_filter()
   /// again afterwards will remove these superfluous conditions.
   ///
+  /// The resulting automaton has a named property "simulated-states", that is a
+  /// vector mapping each state of the input to a state of the output. Note that
+  /// some input states may be mapped to -1, as a by-product of improved
+  /// determinism. Typically, if the language of q1 is included in the language
+  /// of q2, only a transition to q2 will be built.
+  ///
   /// \param automaton the automaton to simulate.
   /// \return a new automaton which is at worst a copy of the received
   /// one
diff --git a/tests/python/simstate.py b/tests/python/simstate.py
index ec8a8aea8..96eaea273 100644
--- a/tests/python/simstate.py
+++ b/tests/python/simstate.py
@@ -166,3 +166,23 @@ State: 11 "{₀[1#1]{₁[0#0,0#1]{₂[1#0]₂}₁}₀}"
 [0&1] 9 {1}
 [!0&1] 1 {1}
 --END--"""
+
+a = spot.translate('!Gp0 xor FG((p0 W Gp1) M p1)')
+a = spot.degeneralize_tba(a)
+b = spot.simulation(a)
+b.set_init_state(1)
+b.purge_unreachable_states()
+b.copy_state_names_from(a)
+assert b.to_str() == """HOA: v1
+States: 1
+Start: 0
+AP: 2 "p0" "p1"
+acc-name: Buchi
+Acceptance: 1 Inf(0)
+properties: trans-labels explicit-labels trans-acc complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0 "[1,8,9]"
+[1] 0
+[!1] 0 {0}
+--END--"""