diff --git a/trio/_core/_parking_lot.py b/trio/_core/_parking_lot.py
index 8b114b5230..a75c81c81d 100644
--- a/trio/_core/_parking_lot.py
+++ b/trio/_core/_parking_lot.py
@@ -85,7 +85,7 @@ class _ParkingLotStatistics:
     tasks_waiting = attr.ib()
 
 
-@attr.s(eq=False, hash=False)
+@attr.s(eq=False, hash=False, slots=True)
 class ParkingLot(metaclass=Final):
     """A fair wait queue with cancellation and requeueing.
 
diff --git a/trio/_sync.py b/trio/_sync.py
index bed339ef6b..68f3e82b05 100644
--- a/trio/_sync.py
+++ b/trio/_sync.py
@@ -10,7 +10,7 @@
 from ._util import Final
 
 
-@attr.s(repr=False, eq=False, hash=False)
+@attr.s(repr=False, eq=False, hash=False, slots=True)
 class Event(metaclass=Final):
     """A waitable boolean value useful for inter-task synchronization,
     inspired by :class:`threading.Event`.