diff --git a/NEWS b/NEWS
index 827a300df..dfbb36451 100644
--- a/NEWS
+++ b/NEWS
@@ -72,6 +72,14 @@ New in spot 2.3.2.dev (not yet released)
     synonym for spot::twa::prop_universal() to help backward
     compatibility.
 
+  Deprecation notice:
+
+  - spot::dtwa_complement() used to work only on deterministic
+    automatons. Due to the recent implementation of spot::dualize(),
+    that does the same job but on any type of automaton,
+    spot::dtwa_complement() is now kept as a proxy of spot::dualize()
+    in order to help backward compatibility, but is now deprecated.
+
 New in spot 2.3.2 (2017-03-15)
 
   Tools:
diff --git a/bench/stutter/stutter_invariance_randomgraph.cc b/bench/stutter/stutter_invariance_randomgraph.cc
index e0a55e8ad..be2a7ff64 100644
--- a/bench/stutter/stutter_invariance_randomgraph.cc
+++ b/bench/stutter/stutter_invariance_randomgraph.cc
@@ -19,7 +19,7 @@
 
 #include <spot/misc/timer.hh>
 #include <spot/tl/apcollect.hh>
-#include <spot/twaalgos/complement.hh>
+#include <spot/twaalgos/dualize.hh>
 #include <spot/twaalgos/remfin.hh>
 #include <spot/twaalgos/randomgraph.hh>
 #include <spot/twaalgos/dot.hh>
@@ -81,7 +81,7 @@ main(int argc, char** argv)
 					  true);
 	    }
 	  while (a->is_empty());
-	  auto na = spot::remove_fin(spot::dtwa_complement(a));
+	  auto na = spot::remove_fin(spot::dualize(a));
 
 	  std::cout << d << ',' << props_n << ',' << seed;
 	  stats.print(a);
diff --git a/bin/autfilt.cc b/bin/autfilt.cc
index be2ef6537..ce24b1c4f 100644
--- a/bin/autfilt.cc
+++ b/bin/autfilt.cc
@@ -60,7 +60,7 @@
 #include <spot/twaalgos/remfin.hh>
 #include <spot/twaalgos/cleanacc.hh>
 #include <spot/twaalgos/dtwasat.hh>
-#include <spot/twaalgos/complement.hh>
+#include <spot/twaalgos/dualize.hh>
 #include <spot/twaalgos/strength.hh>
 #include <spot/twaalgos/hoa.hh>
 #include <spot/twaalgos/sccinfo.hh>
@@ -601,7 +601,7 @@ parse_opt(int key, char* arg, struct argp_state*)
         error(2, 0, "only one --equivalent-to option can be given");
       opt->equivalent_pos = read_automaton(arg, opt->dict);
       opt->equivalent_neg =
-        spot::dtwa_complement(ensure_deterministic(opt->equivalent_pos, true));
+        spot::dualize(ensure_deterministic(opt->equivalent_pos, true));
       break;
     case OPT_GENERALIZED_RABIN:
       if (arg)
@@ -675,7 +675,7 @@ parse_opt(int key, char* arg, struct argp_state*)
     case OPT_INCLUDED_IN:
       {
         auto aut = ensure_deterministic(read_automaton(arg, opt->dict), true);
-        aut = spot::dtwa_complement(aut);
+        aut = spot::dualize(aut);
         if (!opt->included_in)
           opt->included_in = aut;
         else
@@ -1159,7 +1159,7 @@ namespace
         matched &= !aut->intersects(opt->included_in);
       if (opt->equivalent_pos)
         matched &= !aut->intersects(opt->equivalent_neg)
-          && (!dtwa_complement(ensure_deterministic(aut, true))->
+          && (!dualize(ensure_deterministic(aut, true))->
               intersects(opt->equivalent_pos));
 
       if (matched && !opt->acc_words.empty())
@@ -1247,7 +1247,7 @@ namespace
         }
 
       if (opt_complement)
-        aut = spot::dtwa_complement(ensure_deterministic(aut));
+        aut = spot::dualize(ensure_deterministic(aut));
 
       aut = post.run(aut, nullptr);
 
diff --git a/bin/ltlcross.cc b/bin/ltlcross.cc
index 5cbed97a1..d8408b533 100644
--- a/bin/ltlcross.cc
+++ b/bin/ltlcross.cc
@@ -54,7 +54,7 @@
 #include <spot/twaalgos/sccinfo.hh>
 #include <spot/twaalgos/isweakscc.hh>
 #include <spot/twaalgos/word.hh>
-#include <spot/twaalgos/complement.hh>
+#include <spot/twaalgos/dualize.hh>
 #include <spot/twaalgos/cleanacc.hh>
 #include <spot/twaalgos/alternation.hh>
 #include <spot/misc/formater.hh>
@@ -1169,7 +1169,7 @@ namespace
                                 unsigned i)
             {
               if (!no_complement && x[i] && is_deterministic(x[i]))
-                comp[i] = dtwa_complement(x[i]);
+                comp[i] = dualize(x[i]);
             };
 
           for (unsigned i = 0; i < m; ++i)
@@ -1199,7 +1199,7 @@ namespace
                       p.set_type(spot::postprocessor::Generic);
                       p.set_pref(spot::postprocessor::Deterministic);
                       p.set_level(spot::postprocessor::Low);
-                      to[i] = dtwa_complement(p.run(from[i]));
+                      to[i] = dualize(p.run(from[i]));
                       if (verbose)
                         {
                           std::cerr << "info:   " << prefix << i << "\t(";
diff --git a/doc/org/upgrade2.org b/doc/org/upgrade2.org
index 942b05eaf..f9b461084 100644
--- a/doc/org/upgrade2.org
+++ b/doc/org/upgrade2.org
@@ -324,7 +324,7 @@ that provide a function with a similar service.
 | ~tgba/tgbabddfactory.hh~           |                                    | not supported anymore                            |
 | ~tgba/tgbaexplicit.hh~             | ~spot/twa/twagraph.hh~             |                                                  |
 | ~tgba/tgba.hh~                     | ~spot/twa/twa.hh~                  |                                                  |
-| ~tgba/tgbakvcomplement.hh~         |                                    | use ~tgba_determinize()~ and ~dtwa_complement()~ |
+| ~tgba/tgbakvcomplement.hh~         |                                    | use ~tgba_determinize()~ and ~dualize()~         |
 | ~tgba/tgbamask.hh~                 | ~spot/twa/tgbamask.hh~             |                                                  |
 | ~tgba/tgbaproduct.hh~              | ~spot/twa/tgbaproduct.hh~          |                                                  |
 | ~tgba/tgbaproxy.hh~                |                                    | not supported anymore                            |
@@ -333,7 +333,7 @@ that provide a function with a similar service.
 | ~tgba/tgbasgba.hh~                 | ~spot/twaalgos/sbacc.hh~           |                                                  |
 | ~tgba/tgbatba.hh~                  | ~spot/twaalgos/degen.hh~           |                                                  |
 | ~tgba/tgbaunion.hh~                |                                    | not yet reimplemented                            |
-| ~tgba/wdbacomp.hh~                 | ~spot/twaalgos/complement.hh~      | use ~dtwa_complement()~ instead                  |
+| ~tgba/wdbacomp.hh~                 | ~spot/twaalgos/dualize.hh~         | use ~dualize()~ instead                          |
 |------------------------------------+------------------------------------+--------------------------------------------------|
 | ~tgbaparse/public.hh~              | ~spot/parseaut/public.hh~          | single parser for all automata                   |
 
diff --git a/python/spot/impl.i b/python/spot/impl.i
index 4273e61db..be594f45f 100644
--- a/python/spot/impl.i
+++ b/python/spot/impl.i
@@ -532,7 +532,6 @@ def state_is_accepting(self, src) -> "bool":
 %include <spot/twaalgos/dot.hh>
 %include <spot/twaalgos/copy.hh>
 %include <spot/twaalgos/complete.hh>
-%include <spot/twaalgos/complement.hh>
 %feature("flatnested") spot::twa_run::step;
 %include <spot/twaalgos/emptiness.hh>
 %template(list_step) std::list<spot::twa_run::step>;
@@ -570,6 +569,13 @@ def state_is_accepting(self, src) -> "bool":
 %include <spot/twaalgos/word.hh>
 %template(list_bdd) std::list<bdd>;
 
+%pythonprepend spot::twa::dtwa_complement %{
+  from warnings import warn
+  warn("use dualize() instead of dtwa_complement()",
+       DeprecationWarning)
+%}
+
+%include <spot/twaalgos/complement.hh>
 
 %include <spot/parseaut/public.hh>
 
diff --git a/spot/twaalgos/complement.hh b/spot/twaalgos/complement.hh
index 94dbe6b47..0b64b43fa 100644
--- a/spot/twaalgos/complement.hh
+++ b/spot/twaalgos/complement.hh
@@ -36,6 +36,11 @@ namespace spot
   /// Functions like to_generalized_buchi() or remove_fin() are
   /// frequently called after dtwa_complement() to obtain an easier
   /// acceptance condition (maybe at the cost of losing determinism.)
+  ///
+  /// This function was deprecated in spot 2.4. Call the function
+  /// spot::dualize() instead, that is able to complement any input
+  /// automaton, not only deterministic ones.
+  SPOT_DEPRECATED("use spot::dualize() instead")
   SPOT_API twa_graph_ptr
   dtwa_complement(const const_twa_graph_ptr& aut);
 }
diff --git a/spot/twaalgos/langmap.cc b/spot/twaalgos/langmap.cc
index 0899547c2..a457846a6 100644
--- a/spot/twaalgos/langmap.cc
+++ b/spot/twaalgos/langmap.cc
@@ -19,8 +19,8 @@
 
 #include <numeric>
 #include <spot/twa/twa.hh>
-#include <spot/twaalgos/complement.hh>
 #include <spot/twaalgos/copy.hh>
+#include <spot/twaalgos/dualize.hh>
 #include <spot/twaalgos/isdet.hh>
 #include <spot/twaalgos/langmap.hh>
 #include <spot/twaalgos/remfin.hh>
@@ -49,7 +49,7 @@ namespace spot
       alt_init_st_auts[i] = c;
 
       twa_graph_ptr cc =
-        remove_fin(dtwa_complement(copy(c, twa::prop_set::all())));
+        remove_fin(dualize(copy(c, twa::prop_set::all())));
       compl_alt_init_st_auts[i] = cc;
     }
 
diff --git a/spot/twaalgos/minimize.cc b/spot/twaalgos/minimize.cc
index 33c0637d8..01e6ea2f0 100644
--- a/spot/twaalgos/minimize.cc
+++ b/spot/twaalgos/minimize.cc
@@ -44,7 +44,7 @@
 #include <spot/twaalgos/ltl2tgba_fm.hh>
 #include <spot/twaalgos/bfssteps.hh>
 #include <spot/twaalgos/isdet.hh>
-#include <spot/twaalgos/complement.hh>
+#include <spot/twaalgos/dualize.hh>
 #include <spot/twaalgos/remfin.hh>
 
 namespace spot
@@ -661,7 +661,7 @@ namespace spot
           {
             // If the automaton is deterministic, complementing is
             // easy.
-            aut_neg_f = remove_fin(dtwa_complement(aut_f));
+            aut_neg_f = remove_fin(dualize(aut_f));
           }
         else
           {
@@ -681,7 +681,7 @@ namespace spot
       {
         // Complement the minimized WDBA.
         assert((bool)min_aut_f->prop_weak());
-        auto neg_min_aut_f = remove_fin(dtwa_complement(min_aut_f));
+        auto neg_min_aut_f = remove_fin(dualize(min_aut_f));
         if (product(aut_f, neg_min_aut_f)->is_empty())
           // Finally, we are now sure that it was safe
           // to minimize the automaton.
diff --git a/spot/twaalgos/powerset.cc b/spot/twaalgos/powerset.cc
index 6edfcc290..2bc397590 100644
--- a/spot/twaalgos/powerset.cc
+++ b/spot/twaalgos/powerset.cc
@@ -34,7 +34,7 @@
 #include <spot/twaalgos/gtec/gtec.hh>
 #include <spot/twaalgos/sccfilter.hh>
 #include <spot/twaalgos/ltl2tgba_fm.hh>
-#include <spot/twaalgos/complement.hh>
+#include <spot/twaalgos/dualize.hh>
 #include <spot/twaalgos/remfin.hh>
 #include <spot/misc/bitvect.hh>
 #include <spot/misc/bddlt.hh>
@@ -407,7 +407,7 @@ namespace spot
 
     if (product(det, neg_aut)->is_empty())
       // Complement the DBA.
-      if (product(aut, remove_fin(dtwa_complement(det)))->is_empty())
+      if (product(aut, remove_fin(dualize(det)))->is_empty())
         // Finally, we are now sure that it was safe
         // to determinize the automaton.
         return det;
diff --git a/spot/twaalgos/stutter.cc b/spot/twaalgos/stutter.cc
index 6ecb1717a..474ba4d87 100644
--- a/spot/twaalgos/stutter.cc
+++ b/spot/twaalgos/stutter.cc
@@ -27,7 +27,7 @@
 #include <spot/twaalgos/product.hh>
 #include <spot/twaalgos/ltl2tgba_fm.hh>
 #include <spot/twaalgos/isdet.hh>
-#include <spot/twaalgos/complement.hh>
+#include <spot/twaalgos/dualize.hh>
 #include <spot/twaalgos/remfin.hh>
 #include <spot/twaalgos/postproc.hh>
 #include <spot/twa/twaproduct.hh>
@@ -631,7 +631,7 @@ namespace spot
             p.set_level(spot::postprocessor::Low);
             tmp = p.run(aut);
           }
-        neg = dtwa_complement(tmp);
+        neg = dualize(tmp);
       }
 
     is_stut = is_stutter_invariant(make_twa_graph(aut, twa::prop_set::all()),
diff --git a/tests/core/ikwiad.cc b/tests/core/ikwiad.cc
index 73a0e9ac8..3c81ac380 100644
--- a/tests/core/ikwiad.cc
+++ b/tests/core/ikwiad.cc
@@ -57,7 +57,7 @@
 #include <spot/twaalgos/simulation.hh>
 #include <spot/twaalgos/compsusp.hh>
 #include <spot/twaalgos/powerset.hh>
-#include <spot/twaalgos/complement.hh>
+#include <spot/twaalgos/dualize.hh>
 #include <spot/twaalgos/remfin.hh>
 #include <spot/twaalgos/complete.hh>
 #include <spot/twaalgos/dtbasat.hh>
@@ -1146,7 +1146,7 @@ checked_main(int argc, char** argv)
       if (opt_dtwacomp)
         {
           tm.start("DTωA complement");
-          a = remove_fin(dtwa_complement(ensure_digraph(a)));
+          a = remove_fin(dualize(ensure_digraph(a)));
           tm.stop("DTωA complement");
         }
 
diff --git a/tests/python/bugdet.py b/tests/python/bugdet.py
index ea159ecc3..0d84d9d43 100644
--- a/tests/python/bugdet.py
+++ b/tests/python/bugdet.py
@@ -81,11 +81,11 @@ State: 7 {0}
 print("use_simulation=True")
 b1 = spot.tgba_determinize(b, False, True, True, True)
 assert b1.num_states() == 5
-b1 = spot.remove_fin(spot.dtwa_complement(b1))
+b1 = spot.remove_fin(spot.dualize(b1))
 assert not a.intersects(b1);
 
 print("\nuse_simulation=False")
 b2 = spot.tgba_determinize(b, False, True, False, True)
 assert b2.num_states() == 5
-b2 = spot.remove_fin(spot.dtwa_complement(b2))
+b2 = spot.remove_fin(spot.dualize(b2))
 assert not a.intersects(b1);
diff --git a/tests/python/remfin.py b/tests/python/remfin.py
index f09dcf947..02a55dda9 100644
--- a/tests/python/remfin.py
+++ b/tests/python/remfin.py
@@ -19,7 +19,7 @@ State: 2
 --END--
 """)
 aut.prop_inherently_weak(True)
-aut = spot.dtwa_complement(aut)
+aut = spot.dualize(aut)
 aut1 = spot.scc_filter_states(aut)
 assert(aut1.to_str('hoa') == """HOA: v1
 States: 2
diff --git a/tests/python/sum.py b/tests/python/sum.py
index 08f084125..43b96ae94 100644
--- a/tests/python/sum.py
+++ b/tests/python/sum.py
@@ -57,7 +57,7 @@ def produce_phi(rg, n):
 
 def equivalent(a, phi):
   negphi = spot.formula.Not(phi)
-  nega   = spot.dtwa_complement(spot.tgba_determinize(a))
+  nega   = spot.dualize(spot.tgba_determinize(a))
   a2     = spot.ltl_to_tgba_fm(phi, dict)
   nega2  = spot.ltl_to_tgba_fm(negphi, dict)
   return spot.product(a, nega2).is_empty()\