diff --git a/shapiq/approximator/k_sii.py b/shapiq/approximator/k_sii.py
index d795c68b..511cac52 100644
--- a/shapiq/approximator/k_sii.py
+++ b/shapiq/approximator/k_sii.py
@@ -112,8 +112,11 @@ def _calculate_ksii_from_sii(
             `min_order`, and `max_order` parameters. Defaults to `None`.
 
     Returns:
-        The nSII values.
+        The k-SII values.
     """
+    if interaction_lookup is None:
+        interaction_lookup = generate_interaction_lookup(n, 1, max_order)
+
     # compute nSII values from SII values
     bernoulli_numbers = bernoulli(max_order)
     nsii_values = np.zeros_like(sii_values)
@@ -128,8 +131,11 @@ def _calculate_ksii_from_sii(
         # go over all subsets T of length |S| + 1, ..., n that contain S
         for T in powerset(set(range(n)), min_size=interaction_size + 1, max_size=max_order):
             if set(subset).issubset(T):
-                effect_index = interaction_lookup[T]  # get the index of T
-                effect_value = sii_values[effect_index]  # get the effect of T
+                try:
+                    effect_index = interaction_lookup[T]  # get the index of T
+                    effect_value = sii_values[effect_index]  # get the effect of T
+                except KeyError:
+                    effect_value = 0  # if T is not in the interaction_lookup  # TODO: verify this
                 bernoulli_factor = bernoulli_numbers[len(T) - interaction_size]
                 ksii_value += bernoulli_factor * effect_value
         nsii_values[interaction_index] = ksii_value
diff --git a/shapiq/explainer/tree/explainer.py b/shapiq/explainer/tree/explainer.py
index bfaf0ded..fb0aa772 100644
--- a/shapiq/explainer/tree/explainer.py
+++ b/shapiq/explainer/tree/explainer.py
@@ -17,6 +17,7 @@ def __init__(
         model: Union[dict, TreeModel, Any],
         max_order: int = 2,
         min_order: int = 1,
+        interaction_type: str = "k-SII",
         class_label: Optional[int] = None,
         output_type: str = "raw",
     ) -> None:
@@ -34,7 +35,7 @@ def __init__(
 
         # setup explainers for all trees
         self._treeshapiq_explainers: list[TreeSHAPIQ] = [
-            TreeSHAPIQ(model=_tree, max_order=self._max_order, interaction_type="SII")
+            TreeSHAPIQ(model=_tree, max_order=self._max_order, interaction_type=interaction_type)
             for _tree in self._trees
         ]
 
diff --git a/tests/tests_approximators/test_approximator_ksii_estimation.py b/tests/tests_approximators/test_approximator_ksii_estimation.py
index 61ee4c8a..e3cf0cd5 100644
--- a/tests/tests_approximators/test_approximator_ksii_estimation.py
+++ b/tests/tests_approximators/test_approximator_ksii_estimation.py
@@ -70,3 +70,7 @@ def test_nsii_estimation(sii_approximator, ksii_approximator):
     assert isinstance(transformed, np.ndarray)
     with pytest.raises(ValueError):
         _ = transforms_sii_to_ksii(sii_estimates.values)
+    # check with interaction_lookup = None
+    sii_estimates.interaction_lookup = None
+    transformed = transforms_sii_to_ksii(sii_estimates)
+    assert transformed.index == "k-SII"