diff --git a/Lib/functools.py b/Lib/functools.py
index fd33f0ae479ddc..92be41dcf8e9e3 100644
--- a/Lib/functools.py
+++ b/Lib/functools.py
@@ -1026,9 +1026,6 @@ def __init__(self, func):
         self.dispatcher = singledispatch(func)
         self.func = func
 
-        import weakref # see comment in singledispatch function
-        self._method_cache = weakref.WeakKeyDictionary()
-
     def register(self, cls, method=None):
         """generic_method.register(cls, func) -> func
 
@@ -1037,36 +1034,50 @@ def register(self, cls, method=None):
         return self.dispatcher.register(cls, func=method)
 
     def __get__(self, obj, cls=None):
-        if self._method_cache is not None:
-            try:
-                _method = self._method_cache[obj]
-            except TypeError:
-                self._method_cache = None
-            except KeyError:
-                pass
-            else:
-                return _method
+        return _singledispatchmethod_get(self, obj, cls)
 
-        dispatch = self.dispatcher.dispatch
-        funcname = getattr(self.func, '__name__', 'singledispatchmethod method')
-        def _method(*args, **kwargs):
-            if not args:
-                raise TypeError(f'{funcname} requires at least '
-                                '1 positional argument')
-            return dispatch(args[0].__class__).__get__(obj, cls)(*args, **kwargs)
+    @property
+    def __isabstractmethod__(self):
+        return getattr(self.func, '__isabstractmethod__', False)
 
-        _method.__isabstractmethod__ = self.__isabstractmethod__
-        _method.register = self.register
-        update_wrapper(_method, self.func)
 
-        if self._method_cache is not None:
-            self._method_cache[obj] = _method
+class _singledispatchmethod_get:
+    def __init__(self, unbound, obj, cls):
+        self._unbound = unbound
+        self._dispatch = unbound.dispatcher.dispatch
+        self._obj = obj
+        self._cls = cls
+        # Set instance attributes which cannot be handled in __getattr__()
+        # because they conflict with type descriptors.
+        func = unbound.func
+        try:
+            self.__module__ = func.__module__
+        except AttributeError:
+            pass
+        try:
+            self.__doc__ = func.__doc__
+        except AttributeError:
+            pass
+
+    def __call__(self, /, *args, **kwargs):
+        if not args:
+            funcname = getattr(self._unbound.func, '__name__',
+                               'singledispatchmethod method')
+            raise TypeError(f'{funcname} requires at least '
+                            '1 positional argument')
+        return self._dispatch(args[0].__class__).__get__(self._obj, self._cls)(*args, **kwargs)
 
-        return _method
+    def __getattr__(self, name):
+        # Resolve these attributes lazily to speed up creation of
+        # the _singledispatchmethod_get instance.
+        if name not in {'__name__', '__qualname__', '__isabstractmethod__',
+                        '__annotations__', '__type_params__'}:
+            raise AttributeError
+        return getattr(self._unbound.func, name)
 
     @property
-    def __isabstractmethod__(self):
-        return getattr(self.func, '__isabstractmethod__', False)
+    def register(self):
+        return self._unbound.register
 
 
 ################################################################################
diff --git a/Lib/test/test_functools.py b/Lib/test/test_functools.py
index 1b7a76bec839bf..35c6631d908b6e 100644
--- a/Lib/test/test_functools.py
+++ b/Lib/test/test_functools.py
@@ -2900,6 +2900,7 @@ def static_func(arg: int) -> str:
                 """My function docstring"""
                 return str(arg)
 
+        prefix = A.__qualname__ + '.'
         for meth in (
             A.func,
             A().func,
@@ -2909,6 +2910,9 @@ def static_func(arg: int) -> str:
             A().static_func
         ):
             with self.subTest(meth=meth):
+                self.assertEqual(meth.__module__, __name__)
+                self.assertEqual(type(meth).__module__, 'functools')
+                self.assertEqual(meth.__qualname__, prefix + meth.__name__)
                 self.assertEqual(meth.__doc__,
                                  ('My function docstring'
                                   if support.HAVE_DOCSTRINGS
@@ -3241,6 +3245,64 @@ def f(arg):
             def _(arg: undefined):
                 return "forward reference"
 
+    def test_method_equal_instances(self):
+        # gh-127750: Reference to self was cached
+        class A:
+            def __eq__(self, other):
+                return True
+            def __hash__(self):
+                return 1
+            @functools.singledispatchmethod
+            def t(self, arg):
+                return self
+
+        a = A()
+        b = A()
+        self.assertIs(a.t(1), a)
+        self.assertIs(b.t(2), b)
+
+    def test_method_bad_hash(self):
+        class A:
+            def __eq__(self, other):
+                raise AssertionError
+            def __hash__(self):
+                raise AssertionError
+            @functools.singledispatchmethod
+            def t(self, arg):
+                pass
+
+        # Should not raise
+        A().t(1)
+        hash(A().t)
+        A().t == A().t
+
+    def test_method_no_reference_loops(self):
+        # gh-127750: Created a strong reference to self
+        class A:
+            @functools.singledispatchmethod
+            def t(self, arg):
+                return weakref.ref(self)
+
+        a = A()
+        r = a.t(1)
+        self.assertIsNotNone(r())
+        del a  # delete a after a.t
+        if not support.check_impl_detail(cpython=True):
+            support.gc_collect()
+        self.assertIsNone(r())
+
+        a = A()
+        t = a.t
+        del a # delete a before a.t
+        support.gc_collect()
+        r = t(1)
+        self.assertIsNotNone(r())
+        del t
+        if not support.check_impl_detail(cpython=True):
+            support.gc_collect()
+        self.assertIsNone(r())
+
+
 class CachedCostItem:
     _cost = 1
 
diff --git a/Misc/NEWS.d/next/Library/2025-02-11-18-37-26.gh-issue-127750.41SDhF.rst b/Misc/NEWS.d/next/Library/2025-02-11-18-37-26.gh-issue-127750.41SDhF.rst
new file mode 100644
index 00000000000000..b119e296276ac1
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2025-02-11-18-37-26.gh-issue-127750.41SDhF.rst
@@ -0,0 +1,2 @@
+Remove broken :func:`functools.singledispatchmethod` caching introduced in
+:gh:`85160`. Achieve the same performance using different optimization.