diff --git a/src/orion/core/utils/tree.py b/src/orion/core/utils/tree.py
index e128dd12b..443feffbc 100644
--- a/src/orion/core/utils/tree.py
+++ b/src/orion/core/utils/tree.py
@@ -21,85 +21,28 @@
 NodeType = TypeVar("NodeType", bound="TreeNode")
 
 
-# pylint: disable=too-few-public-methods
-class PreOrderTraversal(Iterable[NodeType]):
-    """Iterate on a tree in a pre-order traversal fashion
+def PreOrderTraversal(tree_node: NodeType) -> Iterator[NodeType]:
+    """Iterate on a tree in a pre-order traversal fashion"""
+    stack = [tree_node]
+    while stack:
+        node = stack.pop()
+        yield node
+        stack.extend(node.children[::-1])
 
-    Attributes
-    ----------
-    stack: list of `orion.core.utils.tree.TreeNode`
-        Nodes logged during iteration
-
-    """
-
-    __slots__ = ("stack",)
-
-    def __init__(self, tree_node: NodeType):
-        """Initialize the stack for iteration"""
-        self.stack = [tree_node]
-
-    def __iter__(self) -> Iterator[NodeType]:
-        """Get the iterator"""
-        return self
-
-    def __next__(self) -> NodeType:
-        """Get the next node in pre-order traversal"""
-        try:
-            node = self.stack.pop()
-        except IndexError as exc:
-            raise StopIteration from exc
-
-        self.stack += node.children[::-1]
-
-        return node
-
-
-# pylint: disable=too-few-public-methods
-class DepthFirstTraversal(Iterable[NodeType]):
-    """Iterate on a tree in a pre-order traversal fashion
 
-    Attributes
-    ----------
-    stack: list of `orion.core.utils.tree.TreeNode`
-        Nodes logged during iteration
-    seen: set of `orion.core.utils.tree.TreeNode`
-        Nodes which have been returned during iteration
-
-    """
-
-    __slots__ = ("stack", "seen")
-
-    def __init__(self, tree_node: NodeType):
-        """Initialize the stack and set of seen nodes for iteration"""
-        self.stack = [tree_node]
-        self.seen: set[NodeType] = set()
+def DepthFirstTraversal(tree_node: NodeType) -> Iterable[NodeType]:
+    """Iterate on a tree in a post-order traversal fashion"""
+    seen: set[NodeType] = set()
 
-    def _compute_potential(self) -> list[NodeType]:
-        """Filter out seen nodes from the stack"""
-        if not self.stack:
-            return []
-
-        return list(filter(lambda n: n not in self.seen, self.stack[-1].children))
-
-    def __iter__(self) -> Iterator[NodeType]:
-        """Get the iterator"""
-        return self
-
-    def __next__(self) -> NodeType:
-        """Get the next node in depth-first traversal"""
-        potential = self._compute_potential()
-        while self.stack and potential:
-            self.stack.extend(potential[::-1])
-            potential = self._compute_potential()
-
-        try:
-            node = self.stack.pop()
-        except IndexError as exc:
-            raise StopIteration from exc
-
-        self.seen.add(node)
+    def _inner(node: NodeType) -> Iterable[NodeType]:
+        if node in seen:
+            return
+        seen.add(node)
+        for child in node.children:
+            yield from _inner(child)
+        yield node
 
-        return node
+    return _inner(tree_node)
 
 
 class TreeNode(Generic[T], Iterable[T]):