diff --git a/spot/ltsmin/spins_kripke.hh b/spot/ltsmin/spins_kripke.hh
index 33362d0a0..5cd7cfc03 100644
--- a/spot/ltsmin/spins_kripke.hh
+++ b/spot/ltsmin/spins_kripke.hh
@@ -79,10 +79,6 @@ namespace spot
     }
   };
 
-  /// \brief Shortcut to avoid long names...
-  typedef brick::hashset::FastConcurrent<cspins_state, cspins_state_hasher>
-          cspins_state_map;
-
   /// \brief The management of states (i.e. allocation/deallocation) can
   /// be painless since every time we have to consider wether the state will
   /// be compressed or not. This class aims to simplify this management
@@ -113,7 +109,6 @@ namespace spot
   {
     cspins_state_manager* manager;   // The state manager
     std::vector<cspins_state>* succ; // The successors of a state
-    cspins_state_map map;            // Must be a copy and only one copy/thread
     int* compressed_;
     int* uncompressed_;
     bool compress;
@@ -215,7 +210,6 @@ namespace spot
     bool selfloopize_;
     int dead_idx_;
     std::vector<std::string> aps_;
-    cspins_state_map map_;
     unsigned int nb_threads_;
   };
 
diff --git a/spot/ltsmin/spins_kripke.hxx b/spot/ltsmin/spins_kripke.hxx
index 2e579ae18..eb2e370ca 100644
--- a/spot/ltsmin/spins_kripke.hxx
+++ b/spot/ltsmin/spins_kripke.hxx
@@ -129,10 +129,7 @@ namespace spot
         cspins_state s =
         inner->manager->alloc_setup(dst, inner->compressed_,
                                     inner->manager->size() * 2);
-        auto it = inner->map.insert(s);
-        inner->succ->push_back(*it);
-        if (!it.isnew())
-          inner->manager->dealloc(s);
+        inner->succ->push_back(s);
        },
        &inner);
     if (!n && selfloopize)
@@ -175,10 +172,7 @@ namespace spot
         cspins_state s =
         inner->manager->alloc_setup(dst, inner->compressed_,
                                     inner->manager->size() * 2);
-        auto it = inner->map.insert(s);
-        inner->succ->push_back(*it);
-        if (!it.isnew())
-          inner->manager->dealloc(s);
+        inner->succ->push_back(s);
        },
        &inner);
     if (!n && selfloopize)
@@ -230,7 +224,6 @@ namespace spot
       selfloopize_(selfloopize), aps_(visible_aps),
       nb_threads_(nb_threads)
   {
-    map_.initialSize(2000000);
     manager_ = static_cast<cspins_state_manager*>
       (::operator new(sizeof(cspins_state_manager) * nb_threads));
     inner_ = new inner_callback_parameters[nb_threads_];
@@ -242,7 +235,6 @@ namespace spot
           cspins_state_manager(d_->get_state_size(), compress);
         inner_[i].compressed_ = new int[d_->get_state_size() * 2];
         inner_[i].uncompressed_ = new int[d_->get_state_size()+30];
-        inner_[i].map = map_; // Must be a copy per thread
       }
     dead_idx_ = -1;
     match_aps(visible_aps, dead_prop);