diff --git a/src/twaalgos/safra.cc b/src/twaalgos/safra.cc
index 345820226..95d72f89f 100644
--- a/src/twaalgos/safra.cc
+++ b/src/twaalgos/safra.cc
@@ -37,8 +37,8 @@ namespace spot
       size_t i = 0;
       for (; i < m; ++i)
         {
-          if (lhs[i] < rhs[i])
-            return true;
+          if (lhs[i] != rhs[i])
+            return lhs[i] < rhs[i];
         }
       return lhs.size() > rhs.size();
     }
@@ -255,7 +255,7 @@ namespace spot
     return nodes_ < other.nodes_;
   }
 
-  void safra_state::print_debug(unsigned state_id)
+  void safra_state::print_debug(unsigned state_id) const
   {
     std::cerr << "State: " << state_id << "{ ";
     for (auto& n: nodes_)
diff --git a/src/twaalgos/safra.hh b/src/twaalgos/safra.hh
index 3ccf5912a..09078a22c 100644
--- a/src/twaalgos/safra.hh
+++ b/src/twaalgos/safra.hh
@@ -43,7 +43,8 @@ namespace spot
     typedef std::vector<std::pair<safra_state, unsigned>> succs_t;
     bool operator<(const safra_state& other) const;
     // Print each sub-state with their associated braces of a safra state
-    void print_debug(unsigned state_id);
+    void print_debug(unsigned state_id) const;
+    // Printh the number of states in each brace
     safra_state(unsigned state_number, bool init_state = false);
     // Given a certain transition_label, compute all the successors of that
     // label, and return that new node.