diff --git a/src/misc/acccompl.cc b/src/misc/acccompl.cc
index aee09f31d..3212f5718 100644
--- a/src/misc/acccompl.cc
+++ b/src/misc/acccompl.cc
@@ -21,32 +21,18 @@
 
 namespace spot
 {
-  // The algorithm of this method is simple. We explain this in
-  // bottom/up.
-  // Internally, the bdd is represented like a tree. There is two
-  // output: high(1) and low (0). An acceptance condition is like
-  // the following:
-  // if all has three acceptance conditions, all is equal to
-  // "a!b!c + !ab!c + !a!bc".
-  // So, to compute the negation of an acceptance condition, say "a!b!c"
-  // we need to know wich one is go to one when true. So we are looping
-  // through the conditions until bdd_high is true.
-  // Once found, we keep only it.
-  bdd acc_compl::complement(const bdd acc)
+  // If ALL = a!b!c + !ab!c + !a!bc", the negation of ACC = a!b!c is
+  // RES = bc.   We do that by computing ALL-ACC and enumerating
+  // all positive variables in the remaining products.
+  bdd acc_compl::complement(const bdd& acc)
   {
     bdd_cache_t::const_iterator it = cache_.find(acc);
     if (it != cache_.end())
       return it->second;
 
     bdd res = bddtrue;
-
     bdd n = all_ - acc;
 
-    // This means, if acc == all, the opposite is bddfalse, and not
-    // bddtrue.
-    if (n == bddfalse)
-      res = bddtrue;
-
     while (n != bddfalse)
     {
       bdd cond = bdd_satone(n);
@@ -67,41 +53,27 @@ namespace spot
     return res;
   }
 
-
-  bdd acc_compl::reverse_complement(const bdd acc)
+  bdd acc_compl::reverse_complement(const bdd& acc)
   {
-    // We are sure that if we have no acceptance condition
-    // the result is all_.
+    // We are sure that if we have no acceptance condition the result
+    // is all_.
     if (acc == bddtrue)
       return all_;
 
     // Since we never cache a unique positive bdd, we can reuse the
-    // same cache.
-    // In fact the only kind of acc we will received in this method,
-    // are a conjunction of positive acceptance condition.
-    // I mean: "ab" and not "a!b + !ab"
+    // same cache.  In fact the only kind of acc we will receive in
+    // this method, are a conjunction of positive acceptance
+    // conditions.  (i.e., "ab" and not "a!b + !ab")
     bdd_cache_t::const_iterator it = cache_.find(acc);
     if (it != cache_.end())
       return it->second;
 
     bdd res = all_;
     bdd cond = acc;
-
     while (cond != bddtrue)
     {
-      bdd one;
-
-      one = bdd_ithvar(bdd_var(cond));
-
-      // Because it is a conjunction of positive bdd, we just have to
-      // traverse through the high branch.
+      res &= bdd_nithvar(bdd_var(cond));
       cond = bdd_high(cond);
-
-      // We remove the current `one' from the `neg_' and we associate
-      // `one'.
-      bdd n = bdd_exist(neg_, one) & one;
-
-      res -= n;
     }
 
     cache_[acc] = res;
diff --git a/src/misc/acccompl.hh b/src/misc/acccompl.hh
index af66ed984..b8d30e0f5 100644
--- a/src/misc/acccompl.hh
+++ b/src/misc/acccompl.hh
@@ -35,19 +35,19 @@ namespace spot
   class acc_compl
   {
     public:
-      acc_compl(bdd all, bdd neg)
+      acc_compl(const bdd& all, const bdd& neg)
         : all_(all),
           neg_(neg)
       {
       }
 
 
-      bdd complement(const bdd acc);
-      bdd reverse_complement(const bdd acc);
+      bdd complement(const bdd& acc);
+      bdd reverse_complement(const bdd& acc);
 
     protected:
-      bdd all_;
-      bdd neg_;
+      const bdd all_;
+      const bdd neg_;
       typedef Sgi::hash_map<bdd, bdd, bdd_hash> bdd_cache_t;
       bdd_cache_t cache_;
   };