diff --git a/src/tgbaalgos/cycles.cc b/src/tgbaalgos/cycles.cc
index e6551571f..907e3e636 100644
--- a/src/tgbaalgos/cycles.cc
+++ b/src/tgbaalgos/cycles.cc
@@ -23,9 +23,8 @@
 
 namespace spot
 {
-  enumerate_cycles::enumerate_cycles(const tgba* aut,
-				     const scc_map& map)
-    : aut_(aut), sm_(map)
+  enumerate_cycles::enumerate_cycles(const scc_map& map)
+    : aut_(map.get_aut()), sm_(map)
   {
   }
 
diff --git a/src/tgbaalgos/cycles.hh b/src/tgbaalgos/cycles.hh
index 77d29d431..72ed3bac9 100644
--- a/src/tgbaalgos/cycles.hh
+++ b/src/tgbaalgos/cycles.hh
@@ -63,12 +63,12 @@ namespace spot
   /// dfs_ stack.  Only the last portion of this stack may form a
   /// cycle.
   ///
-  /// The class constructor takes an automaton and an scc_map that
-  /// should already have been built for that automaton.  Calling
-  /// run(n) will enumerate all elementary cycles in SCC #n.  Each
-  /// time an SCC is found, the method cycle_found(s) is called with
-  /// the initial state s of the cycle: the cycle is constituted from
-  /// all the states that are on the dfs_ stack after s (including s).
+  /// The class constructor takes an scc_map that should already have
+  /// been built for its automaton.  Calling run(n) will enumerate all
+  /// elementary cycles in SCC #n.  Each time an SCC is found, the
+  /// method cycle_found(s) is called with the initial state s of the
+  /// cycle: the cycle is constituted from all the states that are on
+  /// the dfs_ stack after s (including s).
   ///
   /// You should inherit from this class and redefine the
   /// cycle_found() method to perform any work you would like to do on
@@ -130,7 +130,7 @@ namespace spot
     dfs_stack dfs_;
 
   public:
-    enumerate_cycles(const tgba* aut, const scc_map& map);
+    enumerate_cycles(const scc_map& map);
 
     /// \brief Run in SCC scc, and call \a cycle_found() for any new
     /// elementary cycle found.
diff --git a/src/tgbaalgos/isweakscc.cc b/src/tgbaalgos/isweakscc.cc
index 5a9dc13c7..19e1e7526 100644
--- a/src/tgbaalgos/isweakscc.cc
+++ b/src/tgbaalgos/isweakscc.cc
@@ -33,8 +33,8 @@ namespace spot
     public:
       bool result;
 
-      weak_checker(const tgba* aut, const scc_map& map)
-	: enumerate_cycles(aut, map), result(true)
+      weak_checker(const scc_map& map)
+	: enumerate_cycles(map), result(true)
       {
       }
 
@@ -66,14 +66,14 @@ namespace spot
   }
 
   bool
-  is_weak_scc(const tgba* aut, scc_map& map, unsigned scc)
+  is_weak_scc(scc_map& map, unsigned scc)
   {
     // If no cycle is accepting, the SCC is weak.
     if (!map.accepting(scc))
       return true;
     // If the SCC is accepting, but one cycle is not, the SCC is not
     // weak.
-    weak_checker w(aut, map);
+    weak_checker w(map);
     w.run(scc);
     return w.result;
   }
diff --git a/src/tgbaalgos/isweakscc.hh b/src/tgbaalgos/isweakscc.hh
index 931bb333d..d28a4b205 100644
--- a/src/tgbaalgos/isweakscc.hh
+++ b/src/tgbaalgos/isweakscc.hh
@@ -28,7 +28,7 @@ namespace spot
   /// \addtogroup tgba_misc
   /// @{
 
-  /// \brief Whether the SCC number \a scc in \a aut is weak.
+  /// \brief Whether the SCC number \a scc in \a map is weak.
   ///
   /// An SCC is weak if either its cycles are all accepting, or they
   /// are all non-accepting.
@@ -38,7 +38,7 @@ namespace spot
   /// whether the SCC is non-accepting already).  For the accepting
   /// SCCs, this function enumerates all cycles in the given SCC (it
   /// stops if it find a non-accepting cycle).
-  bool is_weak_scc(const tgba* aut, scc_map& map, unsigned scc);
+  bool is_weak_scc(scc_map& map, unsigned scc);
 
   /// @}
 }
diff --git a/src/tgbatest/ltl2tgba.cc b/src/tgbatest/ltl2tgba.cc
index 5a0eeb322..6c690ecb1 100644
--- a/src/tgbatest/ltl2tgba.cc
+++ b/src/tgbatest/ltl2tgba.cc
@@ -1425,7 +1425,7 @@ main(int argc, char** argv)
 	      {
 		spot::scc_map m(a);
 		m.build_map();
-		spot::enumerate_cycles c(a, m);
+		spot::enumerate_cycles c(m);
 		unsigned max = m.scc_count();
 		for (unsigned n = 0; n < max; ++n)
 		  {
@@ -1441,7 +1441,7 @@ main(int argc, char** argv)
 		unsigned max = m.scc_count();
 		for (unsigned n = 0; n < max; ++n)
 		  {
-		    bool w = spot::is_weak_scc(a, m, n);
+		    bool w = spot::is_weak_scc(m, n);
 		    std::cout << "SCC #" << n
 			      << (w ? " is weak" : " is not weak")
 			      << std::endl;