diff --git a/NEWS b/NEWS
index e5dac4e3f..c7aba77a9 100644
--- a/NEWS
+++ b/NEWS
@@ -58,6 +58,11 @@ New in spot 2.6.0.dev  (not yet released)
     set.  (This combinations of options is not available from
     command-line tools.)
 
+  - The spot::contains(a, b) function introduced in 2.6 was testing
+    a⊆b instead of a⊇b as one would expect.  Infortunately the
+    documentation was also matching the code, so this is a backward
+    incompatible change.
+
 
 New in spot 2.6  (2018-07-04)
 
diff --git a/bin/autfilt.cc b/bin/autfilt.cc
index 018086289..71ba08ffc 100644
--- a/bin/autfilt.cc
+++ b/bin/autfilt.cc
@@ -1411,7 +1411,7 @@ namespace
         matched &= !aut->intersects(opt->included_in);
       if (opt->equivalent_pos)
         matched &= !aut->intersects(opt->equivalent_neg)
-          && spot::contains(opt->equivalent_pos, aut);
+          && spot::contains(aut, opt->equivalent_pos);
 
       if (matched && !opt->acc_words.empty())
         for (auto& word_aut: opt->acc_words)
diff --git a/python/spot/__init__.py b/python/spot/__init__.py
index b01c21cc8..4980cad3e 100644
--- a/python/spot/__init__.py
+++ b/python/spot/__init__.py
@@ -1047,7 +1047,7 @@ def bdd_to_formula(b, dic=_bdd_dict):
 
 def language_containment_checker(dic=_bdd_dict):
     from spot.impl import language_containment_checker as c
-    c.contains = c.contained
+    c.contains = lambda this, a, b: c.contained(this, b, a)
     c.are_equivalent = c.equal
     return c(dic)
 
diff --git a/spot/twaalgos/contains.cc b/spot/twaalgos/contains.cc
index 957aa41b5..a94b3ac40 100644
--- a/spot/twaalgos/contains.cc
+++ b/spot/twaalgos/contains.cc
@@ -49,25 +49,25 @@ namespace spot
 
   bool contains(const_twa_graph_ptr left, const_twa_graph_ptr right)
   {
-    return !left->intersects(dualize(ensure_deterministic(right)));
+    return !right->intersects(dualize(ensure_deterministic(left)));
   }
 
   bool contains(const_twa_graph_ptr left, formula right)
   {
-    return !left->intersects(translate(formula::Not(right), left->get_dict()));
+    auto right_aut = translate(right, left->get_dict());
+    return !right_aut->intersects(dualize(ensure_deterministic(left)));
   }
 
   bool contains(formula left, const_twa_graph_ptr right)
   {
-    auto left_aut = translate(left, right->get_dict());
-    return !left_aut->intersects(dualize(ensure_deterministic(right)));
+    return !right->intersects(translate(formula::Not(left), right->get_dict()));
   }
 
   bool contains(formula left, formula right)
   {
     auto dict = make_bdd_dict();
-    auto left_aut = translate(left, dict);
-    return !left_aut->intersects(translate(formula::Not(right), dict));
+    auto right_aut = translate(right, dict);
+    return !right_aut->intersects(translate(formula::Not(left), dict));
   }
 
   bool are_equivalent(const_twa_graph_ptr left, const_twa_graph_ptr right)
diff --git a/spot/twaalgos/contains.hh b/spot/twaalgos/contains.hh
index 758339c73..61c53076a 100644
--- a/spot/twaalgos/contains.hh
+++ b/spot/twaalgos/contains.hh
@@ -28,14 +28,14 @@
 namespace spot
 {
   /// \ingroup containment
-  /// \brief Test if the language of \a left is included in that of \a right.
+  /// \brief Test if the language of \a right is included in that of \a left.
   ///
   /// Both arguments can be either formulas or automata.  Formulas
   /// will be converted into automata.
   ///
   /// The inclusion check if performed by ensuring that the automaton
-  /// associated to \a left does not intersect the automaton
-  /// associated to the complement of \a right.  It helps if \a right
+  /// associated to \a right does not intersect the automaton
+  /// associated to the complement of \a left.  It helps if \a left
   /// is a deterministic automaton or a formula (because in both cases
   /// complementation is easier).
   /// @{
diff --git a/tests/python/contains.ipynb b/tests/python/contains.ipynb
index 5e15a0ba1..0e0022b0f 100644
--- a/tests/python/contains.ipynb
+++ b/tests/python/contains.ipynb
@@ -17,7 +17,7 @@
    "source": [
     "# Containement checks\n",
     "\n",
-    "The `spot.contains()` function checks whether the language of its left argument is included in the language of its right argument.  The arguments may mix automata and formulas; the latter can be given as strings."
+    "The `spot.contains()` function checks whether the language of its right argument is included in the language of its left argument.  The arguments may mix automata and formulas; the latter can be given as strings."
    ]
   },
   {
@@ -38,7 +38,7 @@
     {
      "data": {
       "text/plain": [
-       "(False, True)"
+       "(True, False)"
       ]
      },
      "execution_count": 3,
@@ -58,7 +58,7 @@
     {
      "data": {
       "text/plain": [
-       "(False, True)"
+       "(True, False)"
       ]
      },
      "execution_count": 4,
@@ -78,7 +78,7 @@
     {
      "data": {
       "text/plain": [
-       "(False, True)"
+       "(True, False)"
       ]
      },
      "execution_count": 5,
@@ -98,7 +98,7 @@
     {
      "data": {
       "text/plain": [
-       "(False, True)"
+       "(True, False)"
       ]
      },
      "execution_count": 6,
@@ -118,7 +118,7 @@
     {
      "data": {
       "text/plain": [
-       "(False, True)"
+       "(True, False)"
       ]
      },
      "execution_count": 7,
@@ -145,7 +145,7 @@
     {
      "data": {
       "text/plain": [
-       "(False, True)"
+       "(True, False)"
       ]
      },
      "execution_count": 8,
@@ -165,7 +165,7 @@
     {
      "data": {
       "text/plain": [
-       "(False, True)"
+       "(True, False)"
       ]
      },
      "execution_count": 9,
@@ -272,7 +272,7 @@
     {
      "data": {
       "text/plain": [
-       "(False, True)"
+       "(True, False)"
       ]
      },
      "execution_count": 14,
@@ -344,7 +344,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 17,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -360,7 +360,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [
     {
@@ -484,34 +484,6 @@
    "source": [
     "show_one_difference(aut_f, aut_g)"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 36,
-   "metadata": {},
-   "outputs": [
-    {
-     "ename": "NameError",
-     "evalue": "name 'run' is not defined",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-36-d7d1b4bd9ffe>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mrun\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_aut\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[0;31mNameError\u001b[0m: name 'run' is not defined"
-     ]
-    }
-   ],
-   "source": [
-    "run.get_aut()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {