diff --git a/check_linter_assertions.py b/check_linter_assertions.py
index f563553c..3c2008f3 100644
--- a/check_linter_assertions.py
+++ b/check_linter_assertions.py
@@ -158,7 +158,7 @@ def run_linter(linter: str) -> str:
         str: `stdout`.
     """
     p = subprocess.Popen(
-        [linter, source_dir],
+        [sys.executable, "-m", linter, source_dir],
         stdout=subprocess.PIPE,
         stderr=subprocess.PIPE,
     )
diff --git a/plum/dispatcher.py b/plum/dispatcher.py
index bf018c39..9d489e2c 100644
--- a/plum/dispatcher.py
+++ b/plum/dispatcher.py
@@ -1,4 +1,4 @@
-from typing import Any, Callable, Dict, Optional, Tuple, TypeVar, Union
+from typing import Any, Callable, Dict, Optional, Tuple, TypeVar, Union, overload
 
 from .function import Function
 from .overload import get_overloads
@@ -23,7 +23,21 @@ def __init__(self):
         self.functions: Dict[str, Function] = {}
         self.classes: Dict[str, Dict[str, Function]] = {}
 
-    def __call__(self, method: Optional[T] = None, precedence: int = 0) -> T:
+    @overload
+    def __call__(self, method: Callable[..., Any], precedence: int = 0) -> Function:
+        ...
+
+    @overload
+    def __call__(
+        self, method: None, precedence: int = 0
+    ) -> Callable[[Callable[..., Any]], Function]:
+        ...
+
+    def __call__(
+        self,
+        method: Optional[Callable[..., Any]] = None,
+        precedence: int = 0,
+    ) -> Union[Function, Callable[[Callable[..., Any]], Function]]:
         """Decorator to register for a particular signature.
 
         Args:
diff --git a/plum/function.py b/plum/function.py
index 7b97c006..d255b82e 100644
--- a/plum/function.py
+++ b/plum/function.py
@@ -388,7 +388,7 @@ def _handle_not_found_lookup_error(
             raise ex
         return method, return_type
 
-    def __call__(self, *args, **kw_args):
+    def __call__(self, *args: object, **kw_args: object) -> object:
         method, return_type = self._resolve_method_with_cache(args=args)
         return _convert(method(*args, **kw_args), return_type)
 
diff --git a/tests/typechecked/test_overload.py b/tests/typechecked/test_overload.py
index 47f4795b..cee7ad83 100644
--- a/tests/typechecked/test_overload.py
+++ b/tests/typechecked/test_overload.py
@@ -6,24 +6,24 @@
 
 
 @overload
-def f(x: int) -> int:  # E: pyright(marked as overload)
+def f(x: int, y: int) -> int:  # E: pyright(marked as overload)
     return x
 
 
 @overload
-def f(x: str) -> str:  # E: pyright(marked as overload)
+def f(x: str, y: str) -> str:  # E: pyright(marked as overload)
     return x
 
 
 @dispatch
-def f(x):  # E: pyright(overloaded implementation is not consistent)
+def f(x, y):  # E: pyright(overloaded implementation is not consistent)
     pass
 
 
 def test_overload() -> None:
-    assert f(1) == 1
-    assert f("1") == "1"
+    assert f(1, 2) == 1
+    assert f("1", "2") == "1"
     with pytest.raises(NotFoundLookupError):
         # E: pyright(argument of type "float" cannot be assigned to parameter "x")
         # E: mypy(no overload variant of "f" matches argument type "float")
-        f(1.0)
+        f(1.0, 2.0)