diff --git a/python/mwmatching/algorithm.py b/python/mwmatching/algorithm.py
index ddfbe3c..b529fd4 100644
--- a/python/mwmatching/algorithm.py
+++ b/python/mwmatching/algorithm.py
@@ -389,12 +389,11 @@ class Blossom:
         # "tree_blossoms" is the set of all top-level blossoms that belong
         # to the same alternating tree. The same set instance is shared by
         # all top-level blossoms in the tree.
-        self.tree_blossoms: "Optional[set[Blossom]]" = None
+        self.tree_blossoms: Optional[set[Blossom]] = None
 
         # Each top-level blossom maintains a union-find datastructure
         # containing all vertices in the blossom.
-        self.vertex_set: "UnionFindQueue[Blossom, int]"
-        self.vertex_set = UnionFindQueue(self)
+        self.vertex_set: UnionFindQueue[Blossom, int] = UnionFindQueue(self)
 
         # If this is a top-level unlabeled blossom with an edge to an
         # S-blossom, "delta2_node" is the corresponding node in the delta2
diff --git a/python/mwmatching/datastruct.py b/python/mwmatching/datastruct.py
index 48df054..c887669 100644
--- a/python/mwmatching/datastruct.py
+++ b/python/mwmatching/datastruct.py
@@ -1,5 +1,7 @@
 """Data structures for matching."""
 
+from __future__ import annotations
+
 from typing import Generic, Optional, TypeVar
 
 
@@ -38,7 +40,7 @@ class UnionFindQueue(Generic[_NameT, _ElemT]):
                      "parent", "left", "right")
 
         def __init__(self,
-                     owner: "UnionFindQueue[_NameT2, _ElemT2]",
+                     owner: UnionFindQueue[_NameT2, _ElemT2],
                      data: _ElemT2,
                      prio: float
                      ) -> None:
@@ -47,14 +49,14 @@ class UnionFindQueue(Generic[_NameT, _ElemT]):
             This method should not be called directly.
             Instead, call UnionFindQueue.insert().
             """
-            self.owner: "Optional[UnionFindQueue[_NameT2, _ElemT2]]" = owner
+            self.owner: Optional[UnionFindQueue[_NameT2, _ElemT2]] = owner
             self.data = data
             self.prio = prio
             self.min_node = self
             self.height = 1
-            self.parent: "Optional[UnionFindQueue.Node[_NameT2, _ElemT2]]"
-            self.left: "Optional[UnionFindQueue.Node[_NameT2, _ElemT2]]"
-            self.right: "Optional[UnionFindQueue.Node[_NameT2, _ElemT2]]"
+            self.parent: Optional[UnionFindQueue.Node[_NameT2, _ElemT2]]
+            self.left: Optional[UnionFindQueue.Node[_NameT2, _ElemT2]]
+            self.right: Optional[UnionFindQueue.Node[_NameT2, _ElemT2]]
             self.parent = None
             self.left = None
             self.right = None
@@ -98,9 +100,9 @@ class UnionFindQueue(Generic[_NameT, _ElemT]):
             name: Name to assign to the new queue.
         """
         self.name = name
-        self.tree: "Optional[UnionFindQueue.Node[_NameT, _ElemT]]" = None
-        self.sub_queues: "list[UnionFindQueue[_NameT, _ElemT]]" = []
-        self.split_nodes: "list[UnionFindQueue.Node[_NameT, _ElemT]]" = []
+        self.tree: Optional[UnionFindQueue.Node[_NameT, _ElemT]] = None
+        self.sub_queues: list[UnionFindQueue[_NameT, _ElemT]] = []
+        self.split_nodes: list[UnionFindQueue.Node[_NameT, _ElemT]] = []
 
     def clear(self) -> None:
         """Remove all elements from the queue.
@@ -165,7 +167,7 @@ class UnionFindQueue(Generic[_NameT, _ElemT]):
         return node.min_node.data
 
     def merge(self,
-              sub_queues: "list[UnionFindQueue[_NameT, _ElemT]]"
+              sub_queues: list[UnionFindQueue[_NameT, _ElemT]]
               ) -> None:
         """Merge the specified queues.
 
@@ -712,7 +714,7 @@ class PriorityQueue(Generic[_ElemT]):
 
     def __init__(self) -> None:
         """Initialize an empty queue."""
-        self.heap: "list[PriorityQueue.Node[_ElemT]]" = []
+        self.heap: list[PriorityQueue.Node[_ElemT]] = []
 
     def clear(self) -> None:
         """Remove all elements from the queue.