diff --git a/distributed/client.py b/distributed/client.py
index 46982203530..29aa264f32d 100644
--- a/distributed/client.py
+++ b/distributed/client.py
@@ -4,6 +4,7 @@
 import atexit
 import copy
 import inspect
+import itertools
 import json
 import logging
 import os
@@ -31,7 +32,7 @@
 from tlz import first, groupby, merge, partition_all, valmap
 
 import dask
-from dask.base import collections_to_dsk, normalize_token, tokenize
+from dask.base import collections_to_dsk, tokenize
 from dask.core import flatten, validate_key
 from dask.highlevelgraph import HighLevelGraph
 from dask.optimization import SubgraphCallable
@@ -210,11 +211,15 @@ class Future(WrappedKey):
 
     _cb_executor = None
     _cb_executor_pid = None
+    _counter = itertools.count()
+    # Make sure this stays unique even across multiple processes or hosts
+    _uid = uuid.uuid4().hex
 
-    def __init__(self, key, client=None, inform=True, state=None):
+    def __init__(self, key, client=None, inform=True, state=None, _id=None):
         self.key = key
         self._cleared = False
         self._client = client
+        self._id = _id or (Future._uid, next(Future._counter))
         self._input_state = state
         self._inform = inform
         self._state = None
@@ -499,8 +504,16 @@ def release(self):
             except TypeError:  # pragma: no cover
                 pass  # Shutting down, add_callback may be None
 
+    @staticmethod
+    def make_future(key, id):
+        # Can't use kwargs in pickle __reduce__ methods
+        return Future(key=key, _id=id)
+
     def __reduce__(self) -> str | tuple[Any, ...]:
-        return Future, (self.key,)
+        return Future.make_future, (self.key, self._id)
+
+    def __dask_tokenize__(self):
+        return (type(self).__name__, self.key, self._id)
 
     def __del__(self):
         try:
@@ -643,18 +656,6 @@ async def done_callback(future, callback):
     callback(future)
 
 
-@partial(normalize_token.register, Future)
-def normalize_future(f):
-    """Returns the key and the type as a list
-
-    Parameters
-    ----------
-    list
-        The key and the type
-    """
-    return [f.key, type(f)]
-
-
 class AllExit(Exception):
     """Custom exception class to exit All(...) early."""
 
@@ -3434,9 +3435,11 @@ def compute(
 
         if traverse:
             collections = tuple(
-                dask.delayed(a)
-                if isinstance(a, (list, set, tuple, dict, Iterator))
-                else a
+                (
+                    dask.delayed(a)
+                    if isinstance(a, (list, set, tuple, dict, Iterator))
+                    else a
+                )
                 for a in collections
             )
 
diff --git a/distributed/tests/test_client.py b/distributed/tests/test_client.py
index a214bfae840..b30b681d38a 100644
--- a/distributed/tests/test_client.py
+++ b/distributed/tests/test_client.py
@@ -863,11 +863,13 @@ async def test_tokenize_on_futures(c, s, a, b):
     y = c.submit(inc, 1)
     tok = tokenize(x)
     assert tokenize(x) == tokenize(x)
-    assert tokenize(x) == tokenize(y)
+    # Tokens must be unique per instance
+    # See https://github.com/dask/distributed/issues/8561
+    assert tokenize(x) != tokenize(y)
 
     c.futures[x.key].finish()
 
-    assert tok == tokenize(y)
+    assert tok != tokenize(y)
 
 
 @pytest.mark.skipif(not LINUX, reason="Need 127.0.0.2 to mean localhost")