diff --git a/spot/twaalgos/complete.cc b/spot/twaalgos/complete.cc
index 41db648cf..2373eeaf8 100644
--- a/spot/twaalgos/complete.cc
+++ b/spot/twaalgos/complete.cc
@@ -108,6 +108,7 @@ namespace spot
       {
         bdd missingcond = bddtrue;
         acc_cond::mark_t acc = 0U;
+        unsigned edge_to_sink = 0;
         for (auto& t: aut->out(i))
           {
             missingcond -= t.cond;
@@ -125,6 +126,8 @@ namespace spot
             // acceptance sets as the last outgoing edge of the
             // state.
             acc = t.acc;
+            if (t.dst == sink)
+              edge_to_sink = aut->edge_number(t);
           }
         // If the state has incomplete successors, we need to add a
         // edge to some sink state.
@@ -136,11 +139,20 @@ namespace spot
                 sink = aut->new_state();
                 aut->new_edge(sink, sink, bddtrue, um.second);
               }
-            // In case the automaton use state-based acceptance, propagate
-            // the acceptance of the first edge to the one we add.
-            if (aut->prop_state_acc() != true)
-              acc = 0U;
-            aut->new_edge(i, sink, missingcond, acc);
+            // If we already have a brother-edge to the sink,
+            // add the missing condition to that edge.
+            if (edge_to_sink)
+              {
+                aut->edge_data(edge_to_sink).cond |= missingcond;
+              }
+            else                // otherwise, create the new edge.
+              {
+                // in case the automaton use state-based acceptance, propagate
+                // the acceptance of the first edge to the one we add.
+                if (!aut->prop_state_acc().is_true())
+                  acc = 0U;
+                aut->new_edge(i, sink, missingcond, acc);
+              }
           }
       }
 
diff --git a/tests/core/complete.test b/tests/core/complete.test
index c05b436f4..8b2a7f947 100755
--- a/tests/core/complete.test
+++ b/tests/core/complete.test
@@ -1,6 +1,6 @@
 #! /bin/sh
 # -*- coding: utf-8 -*-
-# Copyright (C) 2015, 2016 Laboratoire de Recherche et Développement
+# Copyright (C) 2015-2017 Laboratoire de Recherche et Développement
 # de l'Epita (LRDE).
 #
 # This file is part of Spot, a model checking library.
@@ -152,11 +152,9 @@ properties: trans-labels explicit-labels state-acc complete
 properties: deterministic
 --BODY--
 State: 0
-[0] 1
-[!0] 1
+[t] 1
 State: 1
-[0] 1
-[!0] 1
+[t] 1
 --END--
 HOA: v1
 States: 3
@@ -186,8 +184,7 @@ properties: trans-labels explicit-labels state-acc complete
 properties: deterministic
 --BODY--
 State: 0
-[0] 1
-[!0] 1
+[t] 1
 State: 1 {0}
 [0] 1
 [!0] 1
@@ -205,8 +202,7 @@ State: 0
 [!0 | 1] 0
 [0&!1] 0&1
 State: 1 {0}
-[0&!1] 1
-[!0 | 1] 1
+[t] 1
 --END--
 HOA: v1
 States: 2
diff --git a/tests/python/dualize.py b/tests/python/dualize.py
index c3601f5b3..768b18359 100755
--- a/tests/python/dualize.py
+++ b/tests/python/dualize.py
@@ -408,13 +408,11 @@ properties: deterministic
 --BODY--
 State: 0
 [0&1] 1
-[0&!1] 2
-[!0] 2
+[!0 | !1] 2
 State: 1 {0}
 [t] 1
 State: 2
-[0] 2
-[!0] 2
+[t] 2
 --END--"""
 
 aut = spot.automaton("""