diff --git a/NEWS b/NEWS
index 39d7047bd..d12c0bb91 100644
--- a/NEWS
+++ b/NEWS
@@ -48,6 +48,9 @@ New in spot 2.3.3.dev (not yet released)
     synonym for spot::twa::prop_universal() to help backward
     compatibility.
 
+  - spot::acc_cond::mark_t::sets() now returns an internal iterable
+    object instead of an std::vector<unsigned>.
+
   Deprecation notice:
 
   - spot::dtwa_complement() used to work only on deterministic
diff --git a/python/spot/impl.i b/python/spot/impl.i
index be594f45f..a5efcd064 100644
--- a/python/spot/impl.i
+++ b/python/spot/impl.i
@@ -787,6 +787,14 @@ def state_is_accepting(self, src) -> "bool":
    }
 }
 
+%extend spot::internal::mark_container {
+  swig::SwigPyIterator* __iter__(PyObject **PYTHON_SELF)
+   {
+      return swig::make_forward_iterator_np(self->begin(), self->begin(),
+				         self->end(), *PYTHON_SELF);
+   }
+}
+
 %extend spot::twa_graph {
   unsigned new_univ_edge(unsigned src, const std::vector<unsigned>& v,
                          bdd cond, acc_cond::mark_t acc = 0U)
diff --git a/spot/parseaut/parseaut.yy b/spot/parseaut/parseaut.yy
index 986183b73..e7169972c 100644
--- a/spot/parseaut/parseaut.yy
+++ b/spot/parseaut/parseaut.yy
@@ -2173,14 +2173,18 @@ static void fix_acceptance(result_& r)
   unsigned base = 0;
   if (both)
     {
-      auto v = both.sets();
-      auto vs = v.size();
-      base = acc.add_sets(vs);
+      base = acc.add_sets(both.count());
       for (auto& t: r.h->aut->edge_vector())
-	if ((t.acc & both) != both)
-	  for (unsigned i = 0; i < vs; ++i)
-	    if (!t.acc.has(v[i]))
-	      t.acc |= acc.mark(base + i);
+        {
+          unsigned i = 0;
+	  if ((t.acc & both) != both)
+            for (unsigned v : both.sets())
+              {
+                if (!t.acc.has(v))
+                  t.acc |= acc.mark(base + i);
+                i++;
+              }
+        }
     }
 
   if (onlyneg || both)
diff --git a/spot/twa/acc.hh b/spot/twa/acc.hh
index 197804d3d..465e90064 100644
--- a/spot/twa/acc.hh
+++ b/spot/twa/acc.hh
@@ -28,6 +28,10 @@
 
 namespace spot
 {
+  namespace internal
+  {
+    class mark_container;
+  }
   class SPOT_API acc_cond
   {
   public:
@@ -297,13 +301,8 @@ namespace spot
           }
       }
 
-      // FIXME: Return some iterable object without building a vector.
-      std::vector<unsigned> sets() const
-      {
-        std::vector<unsigned> res;
-        fill(std::back_inserter(res));
-        return res;
-      }
+      // Returns some iterable object that contains the used sets.
+      spot::internal::mark_container sets() const;
 
       SPOT_API
       friend std::ostream& operator<<(std::ostream& os, mark_t m);
@@ -1243,6 +1242,85 @@ namespace spot
 
   SPOT_API
   std::ostream& operator<<(std::ostream& os, const acc_cond& acc);
+
+  namespace internal
+  {
+    class SPOT_API mark_iterator
+    {
+    public:
+      typedef unsigned value_type;
+      typedef const value_type& reference;
+      typedef const value_type* pointer;
+      typedef std::ptrdiff_t difference_type;
+      typedef std::forward_iterator_tag iterator_category;
+
+      mark_iterator() noexcept
+        : m_(0U)
+      {
+      }
+
+      mark_iterator(acc_cond::mark_t m) noexcept
+        : m_(m)
+      {
+      }
+
+      bool operator==(mark_iterator m) const
+      {
+        return m_ == m.m_;
+      }
+
+      bool operator!=(mark_iterator m) const
+      {
+        return m_ != m.m_;
+      }
+
+      value_type operator*() const
+      {
+        SPOT_ASSERT(m_);
+        return m_.min_set() - 1;
+      }
+
+      mark_iterator operator++()
+      {
+        m_.id &= m_.id - 1;
+        return *this;
+      }
+
+      mark_iterator operator++(int)
+      {
+        mark_iterator it = *this;
+        ++(*this);
+        return it;
+      }
+    private:
+      acc_cond::mark_t m_;
+    };
+
+    class SPOT_API mark_container
+    {
+    public:
+      mark_container(spot::acc_cond::mark_t m) noexcept
+        : m_(m)
+      {
+      }
+
+      mark_iterator begin() const
+      {
+        return {m_};
+      }
+      mark_iterator end() const
+      {
+        return {};
+      }
+    private:
+      spot::acc_cond::mark_t m_;
+    };
+  }
+
+  inline spot::internal::mark_container acc_cond::mark_t::sets() const
+  {
+    return {*this};
+  }
 }
 
 namespace std
diff --git a/tests/python/acc_cond.ipynb b/tests/python/acc_cond.ipynb
index b18513672..c371ba95b 100644
--- a/tests/python/acc_cond.ipynb
+++ b/tests/python/acc_cond.ipynb
@@ -15,10 +15,9 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.4.3+"
+   "version": "3.5.3"
   },
-  "name": "",
-  "signature": "sha256:9abaa081794db5d5479c8c9c179c8518aa52b60abdb4b7a106045646e277d43a"
+  "name": ""
  },
  "nbformat": 3,
  "nbformat_minor": 0,
@@ -338,7 +337,7 @@
      "collapsed": false,
      "input": [
       "print(x)\n",
-      "print(x.sets())\n",
+      "print(list(x.sets()))\n",
       "for s in x.sets():\n",
       "    print(s)"
      ],
@@ -350,7 +349,7 @@
        "stream": "stdout",
        "text": [
         "{0,2,5}\n",
-        "(0, 2, 5)\n",
+        "[0, 2, 5]\n",
         "0\n",
         "2\n",
         "5\n"
@@ -1435,10 +1434,10 @@
      "language": "python",
      "metadata": {},
      "outputs": [],
-     "prompt_number": 52
+     "prompt_number": null
     }
    ],
    "metadata": {}
   }
  ]
-}
\ No newline at end of file
+}