diff --git a/spot/twaalgos/zlktree.cc b/spot/twaalgos/zlktree.cc
index 93d7fae55..34c9505ff 100644
--- a/spot/twaalgos/zlktree.cc
+++ b/spot/twaalgos/zlktree.cc
@@ -20,13 +20,15 @@
 #include "config.h"
 #include <iostream>
 #include <spot/twaalgos/zlktree.hh>
+#include <spot/twaalgos/sccinfo.hh>
+#include <deque>
 #include "spot/priv/bddalloc.hh"
 
 namespace spot
 {
-  zielonka_tree::zielonka_tree(acc_cond& cond)
+  zielonka_tree::zielonka_tree(const acc_cond& cond)
   {
-    acc_cond::acc_code& code = cond.get_acceptance();
+    const acc_cond::acc_code& code = cond.get_acceptance();
     auto used = code.used_sets();
     unsigned c = used.count();
     unsigned max = used.max_set();
@@ -225,4 +227,124 @@ namespace spot
       }
     return {branch, lvl};
   }
+
+  namespace
+  {
+    // A state in the zielonka_tree_transform output corresponds to a
+    // state in the input associated to a branch of the tree.
+    typedef std::pair<unsigned, unsigned> zlk_state;
+
+    struct zlk_state_hash
+    {
+      size_t
+      operator()(const zlk_state& s) const noexcept
+      {
+        return wang32_hash(s.first ^ wang32_hash(s.second));
+      }
+    };
+  }
+
+  twa_graph_ptr
+  zielonka_tree_transform(const const_twa_graph_ptr& a)
+  {
+    auto res = make_twa_graph(a->get_dict());
+    res->copy_ap_of(a);
+    zielonka_tree zlk(a->get_acceptance());
+
+    // Preserve determinism, weakness, and stutter-invariance
+    res->prop_copy(a, { false, true, true, true, true, true });
+
+    auto orig_states = new std::vector<unsigned>();
+    auto branches = new std::vector<unsigned>();
+    unsigned ns = a->num_states();
+    orig_states->reserve(ns); // likely more are needed.
+    res->set_named_prop("original-states", orig_states);
+    res->set_named_prop("degen-levels", branches);
+
+    // Associate each zlk_state to its number.
+    typedef std::unordered_map<zlk_state, unsigned, zlk_state_hash> zs2num_map;
+    zs2num_map zs2num;
+
+    // Queue of states to be processed.
+    std::deque<zlk_state> todo;
+
+    auto new_state = [&](zlk_state zs)
+    {
+      if (auto i = zs2num.find(zs); i != zs2num.end())
+        return i->second;
+
+      unsigned ns = res->new_state();
+      zs2num[zs] = ns;
+      todo.emplace_back(zs);
+
+      unsigned orig = zs.first;
+      assert(ns == orig_states->size());
+      orig_states->emplace_back(orig);
+      branches->emplace_back(zs.second);
+      return ns;
+    };
+
+    zlk_state s(a->get_init_state_number(), zlk.first_branch());
+    new_state(s);
+    unsigned max_color = 0;
+    while (!todo.empty())
+      {
+        s = todo.front();
+        todo.pop_front();
+        int src = zs2num[s];
+        unsigned branch = s.second;
+
+        for (auto& i: a->out(s.first))
+          {
+            auto [newbranch, prio] = zlk.step(branch, i.acc);
+            zlk_state d(i.dst, newbranch);
+            unsigned dst = new_state(d);
+            max_color = std::max(max_color, prio);
+            res->new_edge(src, dst, i.cond, {prio});
+          }
+      }
+
+    res->set_acceptance(max_color + 1,
+                        acc_cond::acc_code::parity_min(!zlk.is_even(),
+                                                       max_color + 1));
+
+    // compose original-states with the any previously existing one.
+    // We do that now, because for the bottommost copy below, it's better
+    // if we compose everything.
+    if (auto old_orig_states =
+        a->get_named_prop<std::vector<unsigned>>("original-states"))
+      for (auto& s: *orig_states)
+        s = (*old_orig_states)[s];
+
+    // Now we will iterate over the SCCs in topological order to
+    // remember the "bottommost" SCCs that contain each original
+    // state.  If an original state is duplicated in a higher SCC,
+    // it can be shunted away.  Amen.
+    scc_info si_res(res, scc_info_options::TRACK_STATES);
+    unsigned res_scc_count = si_res.scc_count();
+    unsigned maxorig = *std::max_element(orig_states->begin(),
+                                         orig_states->end());
+    std::vector<unsigned> bottommost_occurence(maxorig + 1);
+    {
+      unsigned n = res_scc_count;
+      do
+        for (unsigned s: si_res.states_of(--n))
+          bottommost_occurence[(*orig_states)[s]] = s;
+      while (n);
+    }
+    unsigned res_ns = res->num_states();
+    std::vector<unsigned> retarget(res_ns);
+    for (unsigned n = 0; n < res_ns; ++n)
+      {
+        unsigned other = bottommost_occurence[(*orig_states)[n]];
+        retarget[n] =
+          (si_res.scc_of(n) != si_res.scc_of(other)) ? other : n;
+      }
+    for (auto& e: res->edges())
+      e.dst = retarget[e.dst];
+    res->set_init_state(retarget[res->get_init_state_number()]);
+    res->purge_unreachable_states();
+
+    return res;
+  }
 }
diff --git a/spot/twaalgos/zlktree.hh b/spot/twaalgos/zlktree.hh
index 1552350b8..b67096f0c 100644
--- a/spot/twaalgos/zlktree.hh
+++ b/spot/twaalgos/zlktree.hh
@@ -37,7 +37,7 @@ namespace spot
   {
   public:
     /// \brief Build a Zielonka tree from the acceptance condition.
-    zielonka_tree(acc_cond& cond);
+    zielonka_tree(const acc_cond& cond);
 
     /// \brief The number of branches in the Zielonka tree.
     ///
@@ -129,4 +129,17 @@ namespace spot
     bool has_streett_shape_ = true;
   };
 
+  /// \ingroup twa_acc_transform
+  /// \brief Paritize an automaton using Zielonka tree.
+  ///
+  /// This corresponds to the application of Section 3 of
+  /// \cite casares.21.icalp
+  ///
+  /// The resulting automaton has a parity acceptance that is either
+  /// "min odd" or "min even", depending on the original acceptance.
+  /// It may uses up to n+1 colors if the input automaton has n
+  /// colors.  Finally, it is colored, i.e., each output transition
+  /// has exactly one color.
+  SPOT_API
+  twa_graph_ptr zielonka_tree_transform(const const_twa_graph_ptr& aut);
 }
diff --git a/tests/python/_zlktree.ipynb b/tests/python/_zlktree.ipynb
index 15c3a8dbc..288f8d2f4 100644
--- a/tests/python/_zlktree.ipynb
+++ b/tests/python/_zlktree.ipynb
@@ -191,7 +191,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fefb0897c00> >"
+       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7efe7807fa80> >"
       ]
      },
      "metadata": {},
@@ -755,7 +755,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fefb10dd300> >"
+       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7efe7807fab0> >"
       ]
      },
      "metadata": {},
@@ -1111,7 +1111,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fefb083c900> >"
+       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7efe6a301e70> >"
       ]
      },
      "metadata": {},
@@ -1247,7 +1247,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fefb08a46f0> >"
+       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7efe6a301e10> >"
       ]
      },
      "metadata": {},
@@ -1358,7 +1358,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fefb08a48a0> >"
+       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7efe6a301840> >"
       ]
      },
      "metadata": {},
@@ -1421,7 +1421,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fefb08a43f0> >"
+       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7efe6a301300> >"
       ]
      },
      "metadata": {},
@@ -1484,7 +1484,7 @@
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7fefb08a43c0> >"
+       "<spot.zielonka_tree; proxy of <Swig Object of type 'spot::zielonka_tree *' at 0x7efe6a305780> >"
       ]
      },
      "metadata": {},
@@ -1511,10 +1511,741 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 19,
    "id": "interesting-seller",
    "metadata": {},
    "outputs": [],
+   "source": [
+    "a = spot.automaton(\"\"\"HOA: v1 name: \"(FGp0 & ((XFp0 & F!p1) | F(Gp1 &\n",
+    "XG!p0))) | G(F!p0 & (XFp0 | F!p1) & F(Gp1 | G!p0))\" States: 14 Start:\n",
+    "0 AP: 2 \"p1\" \"p0\" Acceptance: 6 (Fin(0) & Fin(1)) | ((Fin(4)|Fin(5)) &\n",
+    "(Inf(2)&Inf(3))) properties: trans-labels explicit-labels trans-acc\n",
+    "complete properties: deterministic --BODY-- State: 0 [!0] 1 [0] 2\n",
+    "State: 1 [!0&!1] 1 {0 1 2 3 5} [0&!1] 3 [!0&1] 4 [0&1] 5 State: 2\n",
+    "[0&!1] 2 {1} [!0&1] 4 [!0&!1] 6 [0&1] 7 State: 3 [0&!1] 3 {1 3} [!0&1]\n",
+    "4 [!0&!1] 6 {0 1 2 3 5} [0&1] 8 State: 4 [!0&!1] 4 {1 2 3 5} [!0&1] 4\n",
+    "{2 4 5} [0&!1] 5 {1 3} [0&1] 5 {4} State: 5 [!0&1] 4 {2 4 5} [0&!1] 5\n",
+    "{1 3} [0&1] 8 {2 4} [!0&!1] 9 {1 2 3 5} State: 6 [0&!1] 3 {1 3} [!0&1]\n",
+    "4 [0&1] 5 [!0&!1] 10 State: 7 [!0&1] 4 [0&!1] 7 {1 3} [!0&!1] 11 [0&1]\n",
+    "12 {0 4} State: 8 [!0&1] 4 {2 4 5} [0&1] 5 {4} [0&!1] 8 {1 3} [!0&!1]\n",
+    "11 {1 3 5} State: 9 [!0&1] 4 {2 4 5} [0&!1] 5 {1 3} [0&1] 5 {4}\n",
+    "[!0&!1] 11 {1 3 5} State: 10 [!0&1] 4 [0&1] 8 [!0&!1] 10 {0 1 2 3 5}\n",
+    "[0&!1] 13 {1 2 3} State: 11 [!0&1] 4 {2 4 5} [0&!1] 8 {1 2 3} [0&1] 8\n",
+    "{2 4} [!0&!1] 11 {1 2 3 5} State: 12 [!0&1] 4 [0&1] 7 {0 2 4} [!0&!1]\n",
+    "9 [0&!1] 12 {1 3} State: 13 [!0&1] 4 [0&1] 5 [!0&!1] 10 {0 1 3 5}\n",
+    "[0&!1] 13 {1 3} --END--\"\"\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "informative-mainland",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "b = spot.zielonka_tree_transform(a)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "angry-comedy",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "33"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "b.num_states()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "contained-combat",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 22,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "a.equivalent_to(b)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "paperback-handle",
+   "metadata": {},
+   "outputs": [
+    {
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+      "text/plain": [
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7efe6a34b960> >"
+      ]
+     },
+     "execution_count": 23,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "c = spot.automaton(\"\"\"\n",
+    "HOA: v1\n",
+    "States: 2\n",
+    "Start: 0\n",
+    "AP: 2 \"p1\" \"p0\"\n",
+    "Acceptance: 5 (Fin(0) & (Fin(3)|Fin(4)) & (Inf(1)&Inf(2))) | Inf(3)\n",
+    "properties: trans-labels explicit-labels trans-acc complete\n",
+    "properties: deterministic stutter-invariant\n",
+    "--BODY--\n",
+    "State: 0\n",
+    "[0&!1] 0 {2 3}\n",
+    "[!0&!1] 0 {2 3 4}\n",
+    "[!0&1] 1\n",
+    "[0&1] 1 {2 4}\n",
+    "State: 1\n",
+    "[!0&!1] 0 {0 2 3 4}\n",
+    "[!0&1] 1 {1}\n",
+    "[0&!1] 1 {2 3}\n",
+    "[0&1] 1 {1 2 4}\n",
+    "--END--\n",
+    "\"\"\"); c"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "id": "tired-webcam",
+   "metadata": {},
+   "outputs": [
+    {
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+    "d = spot.zielonka_tree_transform(c); d"
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+   "cell_type": "code",
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+   "id": "funny-taylor",
+   "metadata": {},
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+      "text/plain": [
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+    "c.equivalent_to(d)"
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+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "liable-update",
+   "metadata": {},
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+       "<!-- 2&#45;&gt;0 -->\n",
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+       "<title>2&#45;&gt;0</title>\n",
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+       "<title>2&#45;&gt;1</title>\n",
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+       "<text text-anchor=\"start\" x=\"208\" y=\"-84.08\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b</text>\n",
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+       "</g>\n",
+       "</g>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<spot.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7efe6a301720> >"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "e = spot.translate('!(GFa -> (GFb & GF(!b & !Xb)))', 'gen', 'det')\n",
+    "f = spot.zielonka_tree_transform(e)\n",
+    "display(e,f)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "complimentary-person",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 27,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "e.equivalent_to(f)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "determined-bankruptcy",
+   "metadata": {},
+   "outputs": [],
    "source": []
   }
  ],