diff --git a/bdms/poisson.py b/bdms/poisson.py
index f61a350..005db3a 100644
--- a/bdms/poisson.py
+++ b/bdms/poisson.py
@@ -191,10 +191,12 @@ class ConstantProcess(HomogeneousProcess):
 
     Args:
         value: Constant rate.
+        attr: The name of the :py:class:`bdms.TreeNode` attribute to access. This
+              is not used by this process, but is included for downstream compatibility.
     """
 
-    def __init__(self, value: float = 1.0):
-        super().__init__()
+    def __init__(self, value: float = 1.0, attr: str = "state"):
+        super().__init__(attr=attr)
         self.value = value
 
     def λ_homogeneous(
diff --git a/bdms/tree.py b/bdms/tree.py
index b493f71..d40c5f3 100644
--- a/bdms/tree.py
+++ b/bdms/tree.py
@@ -500,8 +500,7 @@ def slice(self, t: float, attr: str = "x") -> list[Any]:
             return [getattr(self, attr)]
 
         def is_leaf_fn(node: TreeNode):
-            assert node.up is not None
-            return node.t >= t and node.up.t < t
+            return node.up is not None and (node.up.t < t <= node.t)
 
         return [
             (getattr(node, attr) if node.t == t else getattr(node.up, attr))