diff --git a/NEWS b/NEWS
index c6dd244df..cb068bce8 100644
--- a/NEWS
+++ b/NEWS
@@ -6,6 +6,11 @@ New in spot 2.5.1.dev (not yet released)
     remove from the acceptance condition the parity colors that are
     not used in the automaton.
 
+  - twa_graph::purge_unreachable_states() now takes a function which
+    is called with the new numbering of states. This is useful to
+    update an external structure that references states of the twa
+    that we want to purge.
+
 New in spot 2.5.1 (2018-02-20)
 
   Library:
diff --git a/spot/twa/twagraph.cc b/spot/twa/twagraph.cc
index c3d2671d7..d48261a57 100644
--- a/spot/twa/twagraph.cc
+++ b/spot/twa/twagraph.cc
@@ -231,7 +231,7 @@ namespace spot
     g_.chain_edges_();
   }
 
-  void twa_graph::purge_unreachable_states()
+  void twa_graph::purge_unreachable_states(shift_action* f, void* action_data)
   {
     unsigned num_states = g_.num_states();
     // The TODO vector serves two purposes:
@@ -280,6 +280,9 @@ namespace spot
     if (prop_complete().is_false())
       prop_complete(trival::maybe());
 
+    if (f)
+      (*f)(todo, action_data);
+
     defrag_states(std::move(todo), current);
   }
 
diff --git a/spot/twa/twagraph.hh b/spot/twa/twagraph.hh
index 46d4d506b..9a62564a1 100644
--- a/spot/twa/twagraph.hh
+++ b/spot/twa/twagraph.hh
@@ -576,8 +576,16 @@ namespace spot
     /// purge_dead_states() will remove more states than
     /// purge_unreachable_states(), but it is more costly.
     ///
+    /// You can pass a function to this method, which will be invoked
+    /// with a vector indicating the renumbering of states.
+    /// newst[i] == -1U means that state i is unreachable and thus deleted.
+    /// Otherwise, state i is renumbered newst[i].
+    ///
     /// \see purge_dead_states
-    void purge_unreachable_states();
+    typedef void (*shift_action)(const std::vector<unsigned>& newst,
+                                 void* action_data);
+    void purge_unreachable_states(shift_action* f = nullptr,
+                                  void* action_data = nullptr);
 
     /// \brief Remove unused atomic propositions
     ///
diff --git a/tests/core/tgbagraph.test b/tests/core/tgbagraph.test
index 7f2d73893..3e2e5c873 100755
--- a/tests/core/tgbagraph.test
+++ b/tests/core/tgbagraph.test
@@ -1,6 +1,6 @@
 #!/bin/sh
 # -*- coding: utf-8 -*-
-# Copyright (C) 2014-2017 Laboratoire de Recherche et Développement de
+# Copyright (C) 2014-2018 Laboratoire de Recherche et Développement de
 # l'Epita (LRDE).
 #
 # This file is part of Spot, a model checking library.
@@ -230,6 +230,9 @@ digraph G {
   1 [label="s2"]
   2 [label="s3", style="bold", color="#505050"]
 }
+0 -> deleted
+1 -> deleted
+2 -> 0
 digraph G {
   rankdir=LR
   node [shape="circle"]
diff --git a/tests/core/twagraph.cc b/tests/core/twagraph.cc
index 4a34535f0..a7eae696e 100644
--- a/tests/core/twagraph.cc
+++ b/tests/core/twagraph.cc
@@ -105,7 +105,19 @@ static void f2()
   }
   tg->set_init_state(s3);
   spot::print_dot(std::cout, tg);
-  tg->purge_unreachable_states();
+  void (*action)(const std::vector<unsigned>&, void*) =
+    [](const std::vector<unsigned>& newst, void*)
+    {
+      for (unsigned i = 0; i != newst.size(); ++i)
+        {
+          std::cout << i << " -> ";
+          if (newst[i] == -1U)
+            std::cout << "deleted" << std::endl;
+          else
+            std::cout << newst[i] << std::endl;
+        }
+    };
+  tg->purge_unreachable_states(&action);
   spot::print_dot(std::cout, tg);
 }