diff --git a/NEWS b/NEWS
index 2504817b0..085bdfe34 100644
--- a/NEWS
+++ b/NEWS
@@ -180,6 +180,9 @@ New in spot 2.0.3a (not yet released)
     automata, the error message would report "Comp(Ni)*Comp(Pj)" as
     non-empty while the actual culprit was "Comp(Nj)*Comp(Pi)".
 
+  * Fix some non-deterministic execution of minimize_wdba(), causing
+    test-suite failures with the future G++ 7, and clang 3.9.
+
 New in spot 2.0.3 (2016-07-11)
 
   Bug fixes:
diff --git a/spot/twaalgos/minimize.cc b/spot/twaalgos/minimize.cc
index bb4e427ca..7a80fbf56 100644
--- a/spot/twaalgos/minimize.cc
+++ b/spot/twaalgos/minimize.cc
@@ -49,9 +49,9 @@
 
 namespace spot
 {
-  // FIXME: do we really want to use unordered_set instead of set here?
-  // This calls for benchmarking.
-  typedef state_set hash_set;
+  // This is called hash_set for historical reason, but we need the
+  // order inside hash_set to be deterministic.
+  typedef std::set<const state*, state_ptr_less_than> hash_set;
   typedef state_map<unsigned> hash_map;
 
   namespace
diff --git a/tests/core/acc_word.test b/tests/core/acc_word.test
index 01a61607c..882e72a17 100644
--- a/tests/core/acc_word.test
+++ b/tests/core/acc_word.test
@@ -99,13 +99,13 @@ cat >expected <<EOF
 HOA: v1.1
 name: "Fa & Fb"
 States: 4
-Start: 2
+Start: 3
 AP: 2 "a" "b"
 acc-name: Buchi
 Acceptance: 1 Inf(0)
 properties: trans-labels explicit-labels state-acc complete
 properties: deterministic stutter-invariant terminal
-spot.highlight.edges: 1 3 2 3 5 3 6 3 7 2 8 2
+spot.highlight.edges: 1 3 2 3 4 2 7 3 8 2 9 3
 --BODY--
 State: 0 {0}
 [t] 0
@@ -113,13 +113,13 @@ State: 1
 [1] 0
 [!1] 1
 State: 2
+[0] 0
+[!0] 2
+State: 3
 [0&1] 0
 [0&!1] 1
-[!0&!1] 2
-[!0&1] 3
-State: 3
-[0] 0
-[!0] 3
+[!0&1] 2
+[!0&!1] 3
 --END--
 EOF
 diff expected out