diff --git a/bofire/surrogates/feature_importance.py b/bofire/surrogates/feature_importance.py
index 10d5fb088..46ab0402d 100644
--- a/bofire/surrogates/feature_importance.py
+++ b/bofire/surrogates/feature_importance.py
@@ -48,10 +48,13 @@ def permutation_importance(
         k.name: {feature.key: [] for feature in model.inputs} for k in metrics.keys()
     }
     pred = model.predict(X)
-    original_metrics = {
-        k.name: metrics[k](y[output_key].values, pred[output_key + "_pred"].values)  # type: ignore
-        for k in metrics.keys()
-    }
+    if len(pred) >= 2:
+        original_metrics = {
+            k.name: metrics[k](y[output_key].values, pred[output_key + "_pred"].values)  # type: ignore
+            for k in metrics.keys()
+        }
+    else:
+        original_metrics = {k.name: np.nan for k in metrics.keys()}
 
     for feature in model.inputs:
         for _ in range(n_repeats):
@@ -62,9 +65,13 @@ def permutation_importance(
             pred = model.predict(X_i)
             # compute scores
             for metricenum, metric in metrics.items():
-                prelim_results[metricenum.name][feature.key].append(
-                    metric(y[output_key].values, pred[output_key + "_pred"].values)  # type: ignore
-                )
+                if len(pred) >= 2:
+                    prelim_results[metricenum.name][feature.key].append(
+                        metric(y[output_key].values, pred[output_key + "_pred"].values)  # type: ignore
+                    )
+                else:
+                    prelim_results[metricenum.name][feature.key].append(np.nan)  # type: ignore
+
     # convert dictionaries to dataframe for easier postprocessing and statistics
     # and return
     results = {}
diff --git a/bofire/surrogates/trainable.py b/bofire/surrogates/trainable.py
index ddf3d82e2..c38cd6d3a 100644
--- a/bofire/surrogates/trainable.py
+++ b/bofire/surrogates/trainable.py
@@ -96,6 +96,8 @@ def cross_validate(
             raise NotImplementedError(
                 "Cross validation not implemented for multi-output models"
             )
+        # first filter the experiments based on the model setting
+        experiments = self._preprocess_experiments(experiments)
         n = len(experiments)
         if folds > n:
             warnings.warn(
@@ -117,8 +119,6 @@ def cross_validate(
         # instantiate kfold object
         cv = KFold(n_splits=folds, shuffle=True, random_state=random_state)
         key = self.outputs.get_keys()[0]  # type: ignore
-        # first filter the experiments based on the model setting
-        experiments = self._preprocess_experiments(experiments)
         train_results = []
         test_results = []
         # now get the indices for the split
diff --git a/tests/bofire/surrogates/test_feature_importance.py b/tests/bofire/surrogates/test_feature_importance.py
index b1d77c288..0ddfd9c14 100644
--- a/tests/bofire/surrogates/test_feature_importance.py
+++ b/tests/bofire/surrogates/test_feature_importance.py
@@ -61,6 +61,22 @@ def test_permutation_importance():
         assert list(results[m.name].index) == ["mean", "std"]
 
 
+def test_permutation_importance_nan():
+    model, experiments = get_model_and_data()
+    X = experiments[model.inputs.get_keys()][:1]
+    y = experiments[["y"]][:1]
+    model.fit(experiments=experiments)
+    results = permutation_importance(model=model, X=X, y=y, n_repeats=5)
+    assert isinstance(results, dict)
+    assert len(results) == len(metrics)
+    for m in metrics.keys():
+        assert m.name in results.keys()
+        assert isinstance(results[m.name], pd.DataFrame)
+        assert list(results[m.name].columns) == model.inputs.get_keys()
+        assert list(results[m.name].index) == ["mean", "std"]
+        assert len(results[m.name].dropna()) == 0
+
+
 @pytest.mark.parametrize("use_test", [True, False])
 def test_permutation_importance_hook(use_test):
     model, experiments = get_model_and_data()