diff --git a/src/asynkit/compat.py b/src/asynkit/compat.py
index 385d211..b487c3d 100644
--- a/src/asynkit/compat.py
+++ b/src/asynkit/compat.py
@@ -4,6 +4,7 @@
 from asyncio import AbstractEventLoop, Handle, events
 from contextvars import Context
 from typing import TYPE_CHECKING, Any, Callable, Coroutine, Optional, TypeVar
+from weakref import ReferenceType
 
 """Compatibility routines for earlier asyncio versions"""
 
@@ -13,10 +14,16 @@
 
 T = TypeVar("T")
 
+# The following is needed for mypy to work with Python 3.8
+# which doesn't allow subscripting many types
 if TYPE_CHECKING:
     _TaskAny = asyncio.Task[Any]
+    FutureBool = asyncio.Future[bool]
+    ReferenceTypeTaskAny = ReferenceType[_TaskAny]
 else:
     _TaskAny = asyncio.Task
+    FutureBool = asyncio.Future
+    ReferenceTypeTaskAny = ReferenceType
 
 # create_task() got the name argument in 3.8
 
diff --git a/src/asynkit/experimental/priority.py b/src/asynkit/experimental/priority.py
index bb2d5bc..6a94ef1 100644
--- a/src/asynkit/experimental/priority.py
+++ b/src/asynkit/experimental/priority.py
@@ -25,7 +25,7 @@
 
 from typing_extensions import Literal
 
-from asynkit.compat import LockHelper
+from asynkit.compat import FutureBool, LockHelper, ReferenceTypeTaskAny
 from asynkit.loop.default import task_from_handle
 from asynkit.loop.schedulingloop import AbstractSchedulingLoop
 from asynkit.loop.types import TaskAny
@@ -105,17 +105,13 @@ class PriorityLock(Lock, BasePriorityObject, LockHelper):
     of all waiting Tasks.
     """
 
-    _waiters: Optional[
-        PriorityQueue[
-            float, Tuple[asyncio.Future[bool], weakref.ReferenceType[TaskAny]]
-        ]
-    ]
+    _waiters: Optional[PriorityQueue[float, Tuple[FutureBool, ReferenceTypeTaskAny]]]
 
     def __init__(self) -> None:
         # we use weakrefs to avoid reference cycles.  Tasks _own_ locks,
         # but locks don't own tasks. These are _backrefs_.
         super().__init__()
-        self._owning: Optional[weakref.ReferenceType[TaskAny]] = None
+        self._owning: Optional[ReferenceTypeTaskAny] = None
 
     async def acquire(self) -> Literal[True]:
         """Acquire a lock.
@@ -232,7 +228,7 @@ def propagate_priority(self, from_obj: Any) -> None:
         else:
 
             def key(
-                entry: Tuple[asyncio.Future[bool], weakref.ReferenceType[TaskAny]],
+                entry: Tuple[FutureBool, ReferenceTypeTaskAny],
             ) -> bool:
                 fut, _ = entry
                 return fut is from_obj
@@ -249,7 +245,7 @@ class PriorityCondition(asyncio.Condition, LockHelper):
     def __init__(self, lock: Optional[asyncio.Lock] = None) -> None:
         lock = lock or self.LockType()
         super().__init__(lock=lock)
-        self._waiters: PriorityQueue[float, asyncio.Future[bool]] = PriorityQueue()
+        self._waiters: PriorityQueue[float, FutureBool] = PriorityQueue()
 
     async def wait(self) -> Literal[True]:
         if not self.locked():  # pragma: no cover
diff --git a/tests/experimental/test_priority.py b/tests/experimental/test_priority.py
index ef5dc89..a2d02cd 100644
--- a/tests/experimental/test_priority.py
+++ b/tests/experimental/test_priority.py
@@ -5,10 +5,10 @@
 import pytest
 
 from asynkit.experimental.priority import (
+    DefaultPriorityEventLoop,
     PosPriorityQueue,
     PriorityCondition,
     PriorityLock,
-    DefaultPriorityEventLoop,
     PriorityTask,
 )