diff --git a/distributed/collections.py b/distributed/collections.py
index c25001047f6..b074c353ef1 100644
--- a/distributed/collections.py
+++ b/distributed/collections.py
@@ -53,6 +53,22 @@ def __init__(self, *, key: Callable[[T], Any]):
     def __repr__(self) -> str:
         return f"<{type(self).__name__}: {len(self)} items>"
 
+    def __reduce__(self) -> tuple[Callable, tuple]:
+        heap = [(k, i, v) for k, i, vref in self._heap if (v := vref()) in self._data]
+        return HeapSet._unpickle, (self.key, self._inc, heap)
+
+    @staticmethod
+    def _unpickle(
+        key: Callable[[T], Any], inc: int, heap: list[tuple[Any, int, T]]
+    ) -> HeapSet[T]:
+        self = object.__new__(HeapSet)
+        self.key = key  # type: ignore
+        self._data = {v for _, _, v in heap}
+        self._inc = inc
+        self._heap = [(k, i, weakref.ref(v)) for k, i, v in heap]
+        heapq.heapify(self._heap)
+        return self
+
     def __contains__(self, value: object) -> bool:
         return value in self._data
 
diff --git a/distributed/tests/test_collections.py b/distributed/tests/test_collections.py
index 4fd5e7b1151..9b752b37285 100644
--- a/distributed/tests/test_collections.py
+++ b/distributed/tests/test_collections.py
@@ -1,5 +1,9 @@
 from __future__ import annotations
 
+import operator
+import pickle
+import random
+
 import pytest
 
 from distributed.collections import LRU, HeapSet
@@ -22,19 +26,20 @@ def test_lru():
     assert list(l.keys()) == ["c", "a", "d"]
 
 
-def test_heapset():
-    class C:
-        def __init__(self, k, i):
-            self.k = k
-            self.i = i
+class C:
+    def __init__(self, k, i):
+        self.k = k
+        self.i = i
 
-        def __hash__(self):
-            return hash(self.k)
+    def __hash__(self):
+        return hash(self.k)
 
-        def __eq__(self, other):
-            return isinstance(other, C) and other.k == self.k
+    def __eq__(self, other):
+        return isinstance(other, C) and other.k == self.k
 
-    heap = HeapSet(key=lambda c: c.i)
+
+def test_heapset():
+    heap = HeapSet(key=operator.attrgetter("i"))
 
     cx = C("x", 2)
     cy = C("y", 1)
@@ -150,3 +155,29 @@ def __init__(self, i):
         heap.add(C("unsortable_key", None))
     assert len(heap) == 1
     assert set(heap) == {cx}
+
+
+def test_heapset_pickle():
+    """Test pickle roundtrip for a HeapSet.
+
+    Note
+    ----
+    To make this test work with plain pickle and not need cloudpickle, we had to avoid
+    lambdas and local classes in our test. Here we're testing that HeapSet doesn't add
+    lambdas etc. of its own.
+    """
+    heap = HeapSet(key=operator.attrgetter("i"))
+
+    # The heap contains broken weakrefs
+    for i in range(200):
+        c = C(f"y{i}", random.random())
+        heap.add(c)
+        if random.random() > 0.7:
+            heap.remove(c)
+
+    heap2 = pickle.loads(pickle.dumps(heap))
+    assert len(heap) == len(heap2)
+    # Test that the heap has been re-heapified upon unpickle
+    assert len(heap2._heap) < len(heap._heap)
+    while heap:
+        assert heap.pop() == heap2.pop()
diff --git a/distributed/tests/test_worker_state_machine.py b/distributed/tests/test_worker_state_machine.py
index 667032f6e50..aa67892fa15 100644
--- a/distributed/tests/test_worker_state_machine.py
+++ b/distributed/tests/test_worker_state_machine.py
@@ -2,6 +2,7 @@
 
 import asyncio
 import gc
+import pickle
 from collections.abc import Iterator
 
 import pytest
@@ -163,6 +164,27 @@ def test_WorkerState__to_dict(ws):
     assert actual == expect
 
 
+def test_WorkerState_pickle(ws):
+    """Test pickle round-trip.
+
+    Big caveat
+    ----------
+    WorkerState, on its own, can be serialized with pickle; it doesn't need cloudpickle.
+    A WorkerState extracted from a Worker might, as data contents may only be
+    serializable with cloudpickle. Some objects created externally and not designed
+    for network transfer - namely, the SpillBuffer - may not be serializable at all.
+    """
+    ws.handle_stimulus(
+        AcquireReplicasEvent(
+            who_has={"x": ["127.0.0.1:1235"]}, nbytes={"x": 123}, stimulus_id="s1"
+        )
+    )
+    ws.handle_stimulus(UpdateDataEvent(data={"y": 123}, report=False, stimulus_id="s"))
+    ws2 = pickle.loads(pickle.dumps(ws))
+    assert ws2.tasks.keys() == {"x", "y"}
+    assert ws2.data == {"y": 123}
+
+
 def traverse_subclasses(cls: type) -> Iterator[type]:
     yield cls
     for subcls in cls.__subclasses__():
diff --git a/distributed/worker_state_machine.py b/distributed/worker_state_machine.py
index 7dd3431ef14..40dab843982 100644
--- a/distributed/worker_state_machine.py
+++ b/distributed/worker_state_machine.py
@@ -2,7 +2,6 @@
 
 import abc
 import asyncio
-import functools
 import heapq
 import logging
 import operator
@@ -21,7 +20,7 @@
 )
 from copy import copy
 from dataclasses import dataclass, field
-from functools import lru_cache
+from functools import lru_cache, partial, singledispatchmethod
 from itertools import chain
 from typing import TYPE_CHECKING, Any, ClassVar, Literal, NamedTuple, TypedDict, cast
 
@@ -1086,7 +1085,7 @@ def __init__(
         self.has_what = defaultdict(set)
         self.data_needed = HeapSet(key=operator.attrgetter("priority"))
         self.data_needed_per_worker = defaultdict(
-            lambda: HeapSet(key=operator.attrgetter("priority"))
+            partial(HeapSet[TaskState], key=operator.attrgetter("priority"))
         )
         self.in_flight_workers = {}
         self.busy_workers = set()
@@ -2324,7 +2323,7 @@ def _transitions(self, recommendations: Recs, *, stimulus_id: str) -> Instructio
     # Events #
     ##########
 
-    @functools.singledispatchmethod
+    @singledispatchmethod
     def _handle_event(self, ev: StateMachineEvent) -> RecsInstrs:
         raise TypeError(ev)  # pragma: nocover