diff --git a/pyproject.toml b/pyproject.toml
index b2ccba7..d909ba5 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -49,6 +49,7 @@ dev = [
     "pytest-cov",
     "pytest-xdist",
     "nox",
+    "piqtree",
 ]
 
 [tool.pytest.ini_options]
diff --git a/src/phylim/apps.py b/src/phylim/apps.py
index f777458..38dd3bc 100644
--- a/src/phylim/apps.py
+++ b/src/phylim/apps.py
@@ -9,6 +9,7 @@
 from cogent3.core.tree import PhyloNode
 from cogent3.draw.dendrogram import Dendrogram
 from cogent3.evolve import ns_substitution_model, predicate, substitution_model
+from cogent3.evolve.models import register_model
 from cogent3.evolve.parameter_controller import AlignmentLikelihoodFunction
 from cogent3.evolve.predicate import MotifChange
 
@@ -243,30 +244,23 @@ class phylim_to_model_result:
         this app assume tree object derived from piqtree
     """
 
-    excludes = ["length", "mprobs"]
-
     def __init__(self, stationarity: bool = True) -> None:
         self.stationarity = stationarity
 
     def main(self, tree: PhyloNode) -> model_result:
-        params = tree.get_root().params
-        mprobs = tree.params["mprobs"]
-
-        # build predicates, excluding length and mprobs
-        predicates = [k for k in params.keys() if k not in self.excludes]
-
+        params, predicate_names, motif_probs = _parse_params(tree)
         # decide model type based on number of rates/predicates
-        if len(predicates) < 6:
-            predicates = [predicate.parse(k) for k in predicates]
-            submodel = substitution_model.TimeReversibleNucleotide(
-                predicates=predicates
-            )
+        if tree.params["model"] == "UNREST":
+            submodel = _build_unrest_model(predicate_names)
+            # skip "T/G" since it's reference rate
+            params = [p for p in params if p.get("par_name") != "T/G"]
         else:
-            submodel = _gn_constructor(predicates)
+            submodel = _build_reversible_model(predicate_names)
+
         lf = submodel.make_likelihood_function(tree, aligned=True)
-        lf.set_motif_probs(mprobs)
 
-        # set to stationary as default
+        lf.set_motif_probs(motif_probs)
+        lf.apply_param_rules(params)
         lf.set_param_rule("mprobs", is_constant=self.stationarity)
 
         result = model_result(
@@ -278,21 +272,68 @@ def main(self, tree: PhyloNode) -> model_result:
 
         return result
 
-def _gn_constructor(
-        predicates: list
-    ) -> ns_substitution_model.NonReversibleNucleotide:
-        predicates = [MotifChange(*n.split("/"), forward_only=True).aliased(n)
-        for n, value in predicates.items() if value != 1]
-    
-
-        required = {
-            "optimise_motif_probs": False,
-            "predicates": predicates,
-        }
-        kwargs = {"recode_gaps": True, "model_gaps": False} | required
-        return ns_substitution_model.NonReversibleNucleotide(
-            **kwargs,
-        )
+
+def _parse_params(result: PhyloNode) -> tuple[list[dict], list[str], dict]:
+    param_vals = {}
+    for node in result.preorder(include_self=False):
+        for k, v in node.params.items():
+            value = param_vals.get(k, {})
+            param_vals[k] = value
+            if isinstance(v, float):
+                nodes = value.get(v, [])
+                nodes.append(node.name)
+                value[v] = nodes
+            elif isinstance(v, dict):
+                val = tuple((a, v[a]) for a in sorted(v))
+                nodes = value.get(val, [])
+                nodes.append(node.name)
+                value[val] = nodes
+
+    predicate_names = [n for n in param_vals if n not in ("length", "mprobs")]
+    if len(param_vals.get("mprobs", {})) != 1:
+        raise NotImplementedError("More than one set of motif probabilities")
+
+    motif_probs, _ = param_vals.pop("mprobs", {}).popitem()
+    motif_probs = dict(motif_probs)
+
+    param_rules = []
+    for par_name, values in param_vals.items():
+        if len(values) != 1:
+            raise NotImplementedError(f"Parameter: {par_name!r} has a multiple values.")
+        value, _ = values.popitem()
+        param_rules.append({"par_name": par_name, "init": value})
+
+    return param_rules, predicate_names, motif_probs
+
+
+@register_model("nucleotide")
+def _build_reversible_model(
+    predicate_names: list[str],
+) -> substitution_model.TimeReversibleNucleotide:
+    predicates = [predicate.parse(name) for name in predicate_names]
+    return substitution_model.TimeReversibleNucleotide(predicates=predicates)
+
+
+@register_model("nucleotide")
+def _build_unrest_model(
+    predicate_names: list,
+) -> ns_substitution_model.NonReversibleNucleotide:
+    predicates = [
+        MotifChange(*name.split("/"), forward_only=True).aliased(name)
+        for name in predicate_names
+        if "/" in name and "T/G" not in name  # skip reference rate
+    ]
+    if not predicates:
+        raise ValueError("No valid predicates found for UNREST model")
+
+    required = {
+        "optimise_motif_probs": False,
+        "predicates": predicates,
+    }
+    kwargs = required | {"recode_gaps": True, "model_gaps": False}
+    return ns_substitution_model.NonReversibleNucleotide(
+        **kwargs,
+    )
 
 
 @define_app
diff --git a/tests/test_apps.py b/tests/test_apps.py
index c30296a..ca585e4 100644
--- a/tests/test_apps.py
+++ b/tests/test_apps.py
@@ -138,15 +138,18 @@ def test_check_fit_boundary():
     assert isinstance(res, BoundsViolation)
 
 
-@pytest.mark.parametrize("tree_name", ["hky_tree", "gtr_tree", "unrest_tree"])
-def test_convert_piq_build_treeto_model_result(tree_name):
-    tree = deserialise_object(f"{DATADIR}/piqtree/{tree_name}.json")
+@pytest.mark.xfail(reason="need new version of piqtree")
+@pytest.mark.parametrize("model_name", ["HKY", "GTR", "UNREST"])
+def test_convert_piq_build_treeto_model_result(model_name):
+    fit = get_app("piq_fit_tree", tree=_algn.quick_tree(), model=model_name)
+    tree = fit(_algn)
     converter = phylim_to_model_result()
     res = converter(tree)
     res.lf.set_alignment(_algn)
     assert allclose(res.lf.lnL, tree.params["lnL"])
 
 
+@pytest.mark.xfail(reason="need new version of piqtree")
 @pytest.mark.skipif(
     sys.platform.startswith("win"), reason="Test not supported on Windows"
 )