diff --git a/mypy/checkmember.py b/mypy/checkmember.py
index e75a8ed7a5b03..80813b21408dd 100644
--- a/mypy/checkmember.py
+++ b/mypy/checkmember.py
@@ -1112,6 +1112,10 @@ def f(self: S) -> T: ...
             ),
             ignore_pos_arg_names=True,
         ):
+            if not self_callable and not has_valid_self_type_bounds(
+                item, selfarg, dispatched_arg_type
+            ):
+                continue
             new_items.append(item)
         elif isinstance(selfarg, ParamSpecType):
             # TODO: This is not always right. What's the most reasonable thing to do here?
@@ -1129,6 +1133,46 @@ def f(self: S) -> T: ...
     return Overloaded(new_items)
 
 
+def has_valid_self_type_bounds(
+    item: CallableType, selfarg: ProperType, dispatched_arg_type: Type
+) -> bool:
+    """Check that inferred self type arguments satisfy their bounds/values.
+
+    This only applies to explicit self type variables, so we don't disturb
+    PEP 673 Self handling while still rejecting bounded self types like
+    ``list[SupportsRichComparisonT]`` when the receiver can't satisfy the bound.
+    """
+    if not item.variables or not supported_self_type(selfarg):
+        return True
+
+    self_ids = {tv.id for tv in get_all_type_vars(selfarg)}
+    self_vars = [tv for tv in item.variables if tv.id in self_ids and tv.name != "Self"]
+    if not self_vars:
+        return True
+
+    from mypy.infer import infer_type_arguments
+
+    typeargs = infer_type_arguments(
+        self_vars, selfarg, dispatched_arg_type, is_supertype=True, erase_types=False
+    )
+    return all(
+        self_type_argument_within_bounds(tvar, typ) for tvar, typ in zip(self_vars, typeargs)
+    )
+
+
+def self_type_argument_within_bounds(tvar: TypeVarLikeType, typ: Type | None) -> bool:
+    if typ is None or isinstance(tvar, (ParamSpecType, TypeVarTupleType)):
+        return True
+
+    assert isinstance(tvar, TypeVarType)
+    if tvar.name == "Self":
+        return True
+    if tvar.values:
+        return any(is_subtype(typ, value) for value in tvar.values)
+
+    return is_subtype(typ, tvar.upper_bound)
+
+
 def analyze_class_attribute_access(
     itype: Instance,
     name: str,
diff --git a/test-data/unit/check-selftype.test b/test-data/unit/check-selftype.test
index c157200352562..35f993e844ef8 100644
--- a/test-data/unit/check-selftype.test
+++ b/test-data/unit/check-selftype.test
@@ -749,6 +749,16 @@ def bad(x: str) -> str: ...
 reveal_type(ci.from_item(conv))  # N: Revealed type is "builtins.str"
 ci.from_item(bad)  # E: Argument 1 to "from_item" of "C" has incompatible type "Callable[[str], str]"; expected "Callable[[int], str]"
 
+[case testListSortSelfTypeOverload]
+xs: list[int | None] = [2, None]
+xs.sort()  # E: Missing named argument "key" for "sort" of "list"
+[2, None].sort()  # E: Missing named argument "key" for "sort" of "list"
+xs.sort(key=lambda x: 0)
+
+ys: list[int] = [2, 1]
+ys.sort()
+[builtins fixtures/list-sort-selftype.pyi]
+
 [case testSelfTypeRestrictedMethodOverloadInit]
 from typing import TypeVar
 from lib import P, C
diff --git a/test-data/unit/fixtures/list-sort-selftype.pyi b/test-data/unit/fixtures/list-sort-selftype.pyi
new file mode 100644
index 0000000000000..5644b1c69af43
--- /dev/null
+++ b/test-data/unit/fixtures/list-sort-selftype.pyi
@@ -0,0 +1,48 @@
+# Builtins stub used in list.sort self-type overload tests.
+
+from typing import TypeVar, Iterable, Iterator, Sequence, overload, Callable
+
+T = TypeVar('T')
+SupportsRichComparisonT = TypeVar('SupportsRichComparisonT', bound='SupportsRichComparison')
+
+class object:
+    def __init__(self) -> None: pass
+    def __eq__(self, other: object) -> bool: pass
+
+class SupportsRichComparison:
+    def __lt__(self, other: object) -> bool: pass
+
+class type: pass
+class ellipsis: pass
+
+class list(Sequence[T]):
+    @overload
+    def __init__(self) -> None: pass
+    @overload
+    def __init__(self, x: Iterable[T]) -> None: pass
+    def __iter__(self) -> Iterator[T]: pass
+    def __len__(self) -> int: pass
+    def __contains__(self, item: object) -> bool: pass
+    def __getitem__(self, x: int) -> T: pass
+    @overload
+    def sort(self: list[SupportsRichComparisonT], *, key: None = None, reverse: bool = False) -> None: ...
+    @overload
+    def sort(self, *, key: Callable[[T], SupportsRichComparison], reverse: bool = False) -> None: ...
+
+class tuple(Sequence[T]): pass
+class function: pass
+
+class int(SupportsRichComparison):
+    def __bool__(self) -> bool: pass
+
+class float:
+    def __bool__(self) -> bool: pass
+
+class str:
+    def __len__(self) -> bool: pass
+
+class bool(int): pass
+
+property = object()
+
+class dict: pass