diff --git a/jsonpath_rfc9535/segments.py b/jsonpath_rfc9535/segments.py
index 057a76b..2e0f7e5 100644
--- a/jsonpath_rfc9535/segments.py
+++ b/jsonpath_rfc9535/segments.py
@@ -145,18 +145,20 @@ def _children(node: JSONPathNode) -> Iterable[JSONPathNode]:
         while queue:
             _node, depth = queue.popleft()
 
-            if depth > self.env.max_recursion_depth:
+            if depth >= self.env.max_recursion_depth:
                 raise JSONPathRecursionError(
                     "recursion limit exceeded", token=self.token
                 )
 
             yield _node
+
             # Visit child nodes now or queue them for later?
             visit_children = random.choice([True, False])  # noqa: S311
+
             for child in _children(_node):
                 if visit_children:
                     yield child
-                    queue.extend([(child, depth + 1) for child in _children(child)])
+                    queue.extend([(child, depth + 2) for child in _children(child)])
                 else:
                     queue.append((child, depth + 1))