diff --git a/doc/examples/example_cli_famos.ipynb b/doc/examples/example_cli_famos.ipynb
index a1d32a1..c413cb7 100644
--- a/doc/examples/example_cli_famos.ipynb
+++ b/doc/examples/example_cli_famos.ipynb
@@ -142,7 +142,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "petab_select/candidate_space.py:1137: RuntimeWarning: Model `model_subspace_1-0001011010010010` has been previously excluded from the candidate space so is skipped here.\n",
+      "petab_select/petab_select/candidate_space.py:1142: RuntimeWarning: Model `model_subspace_1-0001011010010010` has been previously excluded from the candidate space so is skipped here.\n",
       "  return_value = self.inner_candidate_space.consider(model)\n"
      ]
     },
diff --git a/doc/examples/workflow_cli.ipynb b/doc/examples/workflow_cli.ipynb
index 6f4cf83..9acf36b 100644
--- a/doc/examples/workflow_cli.ipynb
+++ b/doc/examples/workflow_cli.ipynb
@@ -817,7 +817,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 22,
    "id": "d5d03cd6",
    "metadata": {},
    "outputs": [
@@ -825,7 +825,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "output_cli/best_model_petab/problem.yaml\n"
+      "petab_select/doc/examples/output_cli/best_model_petab/problem.yaml\n"
      ]
     }
    ],
diff --git a/doc/examples/workflow_python.ipynb b/doc/examples/workflow_python.ipynb
index 170c767..cbc7afb 100644
--- a/doc/examples/workflow_python.ipynb
+++ b/doc/examples/workflow_python.ipynb
@@ -230,7 +230,7 @@
    ],
    "source": [
     "local_best_model = petab_select.ui.get_best(\n",
-    "    problem=select_problem, models=iteration_results[MODELS].values()\n",
+    "    problem=select_problem, models=iteration_results[MODELS]\n",
     ")\n",
     "print_model(local_best_model)"
    ]
@@ -322,10 +322,10 @@
     "    problem=select_problem, candidate_space=iteration_results[CANDIDATE_SPACE]\n",
     ")\n",
     "local_best_model = petab_select.ui.get_best(\n",
-    "    problem=select_problem, models=iteration_results[MODELS].values()\n",
+    "    problem=select_problem, models=iteration_results[MODELS]\n",
     ")\n",
     "\n",
-    "for candidate_model in iteration_results[MODELS].values():\n",
+    "for candidate_model in iteration_results[MODELS]:\n",
     "    if candidate_model.get_hash() == local_best_model.get_hash():\n",
     "        print(BOLD_TEXT + \"BEST MODEL OF CURRENT ITERATION\" + NORMAL_TEXT)\n",
     "    print_model(candidate_model)"
@@ -372,10 +372,10 @@
     "    problem=select_problem, candidate_space=iteration_results[CANDIDATE_SPACE]\n",
     ")\n",
     "local_best_model = petab_select.ui.get_best(\n",
-    "    problem=select_problem, models=iteration_results[MODELS].values()\n",
+    "    problem=select_problem, models=iteration_results[MODELS]\n",
     ")\n",
     "\n",
-    "for candidate_model in iteration_results[MODELS].values():\n",
+    "for candidate_model in iteration_results[MODELS]:\n",
     "    if candidate_model.get_hash() == local_best_model.get_hash():\n",
     "        print(BOLD_TEXT + \"BEST MODEL OF CURRENT ITERATION\" + NORMAL_TEXT)\n",
     "    print_model(candidate_model)"
@@ -415,10 +415,10 @@
     "    problem=select_problem, candidate_space=iteration_results[CANDIDATE_SPACE]\n",
     ")\n",
     "local_best_model = petab_select.ui.get_best(\n",
-    "    problem=select_problem, models=iteration_results[MODELS].values()\n",
+    "    problem=select_problem, models=iteration_results[MODELS]\n",
     ")\n",
     "\n",
-    "for candidate_model in iteration_results[MODELS].values():\n",
+    "for candidate_model in iteration_results[MODELS]:\n",
     "    if candidate_model.get_hash() == local_best_model.get_hash():\n",
     "        print(BOLD_TEXT + \"BEST MODEL OF CURRENT ITERATION\" + NORMAL_TEXT)\n",
     "    print_model(candidate_model)"
@@ -501,7 +501,7 @@
    "source": [
     "best_model = petab_select.ui.get_best(\n",
     "    problem=select_problem,\n",
-    "    models=iteration_results[CANDIDATE_SPACE].calibrated_models.values(),\n",
+    "    models=iteration_results[CANDIDATE_SPACE].calibrated_models,\n",
     ")\n",
     "print_model(best_model)"
    ]
diff --git a/petab_select/candidate_space.py b/petab_select/candidate_space.py
index b559bbc..8af42c1 100644
--- a/petab_select/candidate_space.py
+++ b/petab_select/candidate_space.py
@@ -1002,7 +1002,13 @@ def __init__(
         else:
             self.most_distant_max_number = 1
 
-        self.best_models = Models()
+        # TODO update to new `Models` type. Currently problematic because the
+        # order of `best_models` matters. This would be fine for `Models` to
+        # handle, except that `Models._update` will use a pre-existing index
+        # if there is a model with the same hash. FIXME regenerate the expected
+        # FAMoS models when `best_models` never contains duplicate models...
+        # Also add a `sort` method to `Models` to sort by criterion.
+        self.best_models = []
         self.best_model_of_current_run = predecessor_model
 
         self.jumped_to_most_distant = False
diff --git a/petab_select/models.py b/petab_select/models.py
index 49359b4..fa0cf57 100644
--- a/petab_select/models.py
+++ b/petab_select/models.py
@@ -176,7 +176,10 @@ def __setitem__(self, key: ModelIndex, item: ModelLike) -> None:
             self.append(item)
 
     def _update(self, index: int, item: ModelLike) -> None:
-        """Update the models by adding a new model or overwriting an old model.
+        """Update the models by adding a new model, with possible replacement.
+
+        If the instance contains a model with a matching hash, that model
+        will be replaced.
 
         Args:
             index: