diff --git a/numpy-stubs/__init__.pyi b/numpy-stubs/__init__.pyi
index 9151ad1..4c0e847 100644
--- a/numpy-stubs/__init__.pyi
+++ b/numpy-stubs/__init__.pyi
@@ -10,6 +10,7 @@ from typing import (
     Container,
     Callable,
     Dict,
+    Generic,
     IO,
     Iterable,
     List,
@@ -35,6 +36,11 @@ if sys.version_info[0] < 3:
 else:
     from typing import SupportsBytes
 
+if sys.version_info >= (3, 8):
+    from typing import Literal
+else:
+    from typing_extensions import Literal
+
 _Shape = Tuple[int, ...]
 
 # Anything that can be coerced to a shape tuple
@@ -619,7 +625,10 @@ WRAP: int
 little_endian: int
 tracemalloc_domain: int
 
-class ufunc:
+_Nin = TypeVar("_Nin", bound=int)
+_Nout = TypeVar("_Nout", bound=int)
+
+class ufunc(Generic[_Nin], Generic[_Nout]):
     @property
     def __name__(self) -> str: ...
     def __call__(
@@ -646,11 +655,11 @@ class ufunc:
         # int, an int, and a callable, but there's no way to express
         # that.
         extobj: List[Union[int, Callable]] = ...,
-    ) -> Union[ndarray, generic]: ...
+    ) -> Union[ndarray, generic, Tuple[Union[ndarray, generic], ...]]: ...
     @property
-    def nin(self) -> int: ...
+    def nin(self) -> _Nin: ...
     @property
-    def nout(self) -> int: ...
+    def nout(self) -> _Nout: ...
     @property
     def nargs(self) -> int: ...
     @property
@@ -689,92 +698,92 @@ class ufunc:
     @property
     def at(self) -> Any: ...
 
-absolute: ufunc
-add: ufunc
-arccos: ufunc
-arccosh: ufunc
-arcsin: ufunc
-arcsinh: ufunc
-arctan2: ufunc
-arctan: ufunc
-arctanh: ufunc
-bitwise_and: ufunc
-bitwise_or: ufunc
-bitwise_xor: ufunc
-cbrt: ufunc
-ceil: ufunc
-conjugate: ufunc
-copysign: ufunc
-cos: ufunc
-cosh: ufunc
-deg2rad: ufunc
-degrees: ufunc
-divmod: ufunc
-equal: ufunc
-exp2: ufunc
-exp: ufunc
-expm1: ufunc
-fabs: ufunc
-float_power: ufunc
-floor: ufunc
-floor_divide: ufunc
-fmax: ufunc
-fmin: ufunc
-fmod: ufunc
-frexp: ufunc
-gcd: ufunc
-greater: ufunc
-greater_equal: ufunc
-heaviside: ufunc
-hypot: ufunc
-invert: ufunc
-isfinite: ufunc
-isinf: ufunc
-isnan: ufunc
-isnat: ufunc
-lcm: ufunc
-ldexp: ufunc
-left_shift: ufunc
-less: ufunc
-less_equal: ufunc
-log10: ufunc
-log1p: ufunc
-log2: ufunc
-log: ufunc
-logaddexp2: ufunc
-logaddexp: ufunc
-logical_and: ufunc
-logical_not: ufunc
-logical_or: ufunc
-logical_xor: ufunc
-matmul: ufunc
-maximum: ufunc
-minimum: ufunc
-modf: ufunc
-multiply: ufunc
-negative: ufunc
-nextafter: ufunc
-not_equal: ufunc
-positive: ufunc
-power: ufunc
-rad2deg: ufunc
-radians: ufunc
-reciprocal: ufunc
-remainder: ufunc
-right_shift: ufunc
-rint: ufunc
-sign: ufunc
-signbit: ufunc
-sin: ufunc
-sinh: ufunc
-spacing: ufunc
-sqrt: ufunc
-square: ufunc
-subtract: ufunc
-tan: ufunc
-tanh: ufunc
-true_divide: ufunc
-trunc: ufunc
+absolute: ufunc[Literal[1], Literal[1]]
+add: ufunc[Literal[2], Literal[1]]
+arccos: ufunc[Literal[1], Literal[1]]
+arccosh: ufunc[Literal[1], Literal[1]]
+arcsin: ufunc[Literal[1], Literal[1]]
+arcsinh: ufunc[Literal[1], Literal[1]]
+arctan2: ufunc[Literal[2], Literal[1]]
+arctan: ufunc[Literal[1], Literal[1]]
+arctanh: ufunc[Literal[1], Literal[1]]
+bitwise_and: ufunc[Literal[2], Literal[1]]
+bitwise_or: ufunc[Literal[2], Literal[1]]
+bitwise_xor: ufunc[Literal[2], Literal[1]]
+cbrt: ufunc[Literal[1], Literal[1]]
+ceil: ufunc[Literal[1], Literal[1]]
+conjugate: ufunc[Literal[1], Literal[1]]
+copysign: ufunc[Literal[2], Literal[1]]
+cos: ufunc[Literal[1], Literal[1]]
+cosh: ufunc[Literal[1], Literal[1]]
+deg2rad: ufunc[Literal[1], Literal[1]]
+degrees: ufunc[Literal[1], Literal[1]]
+divmod: ufunc[Literal[2], Literal[2]]
+equal: ufunc[Literal[2], Literal[1]]
+exp2: ufunc[Literal[1], Literal[1]]
+exp: ufunc[Literal[1], Literal[1]]
+expm1: ufunc[Literal[1], Literal[1]]
+fabs: ufunc[Literal[1], Literal[1]]
+float_power: ufunc[Literal[2], Literal[1]]
+floor: ufunc[Literal[1], Literal[1]]
+floor_divide: ufunc[Literal[2], Literal[1]]
+fmax: ufunc[Literal[2], Literal[1]]
+fmin: ufunc[Literal[2], Literal[1]]
+fmod: ufunc[Literal[2], Literal[1]]
+frexp: ufunc[Literal[1], Literal[2]]
+gcd: ufunc[Literal[2], Literal[1]]
+greater: ufunc[Literal[2], Literal[1]]
+greater_equal: ufunc[Literal[2], Literal[1]]
+heaviside: ufunc[Literal[2], Literal[1]]
+hypot: ufunc[Literal[2], Literal[1]]
+invert: ufunc[Literal[1], Literal[1]]
+isfinite: ufunc[Literal[1], Literal[1]]
+isinf: ufunc[Literal[1], Literal[1]]
+isnan: ufunc[Literal[1], Literal[1]]
+isnat: ufunc[Literal[1], Literal[1]]
+lcm: ufunc[Literal[2], Literal[1]]
+ldexp: ufunc[Literal[2], Literal[1]]
+left_shift: ufunc[Literal[2], Literal[1]]
+less: ufunc[Literal[2], Literal[1]]
+less_equal: ufunc[Literal[2], Literal[1]]
+log10: ufunc[Literal[1], Literal[1]]
+log1p: ufunc[Literal[1], Literal[1]]
+log2: ufunc[Literal[1], Literal[1]]
+log: ufunc[Literal[1], Literal[1]]
+logaddexp2: ufunc[Literal[2], Literal[1]]
+logaddexp: ufunc[Literal[2], Literal[1]]
+logical_and: ufunc[Literal[2], Literal[1]]
+logical_not: ufunc[Literal[1], Literal[1]]
+logical_or: ufunc[Literal[2], Literal[1]]
+logical_xor: ufunc[Literal[2], Literal[1]]
+matmul: ufunc[Literal[2], Literal[1]]
+maximum: ufunc[Literal[2], Literal[1]]
+minimum: ufunc[Literal[2], Literal[1]]
+modf: ufunc[Literal[1], Literal[2]]
+multiply: ufunc[Literal[2], Literal[1]]
+negative: ufunc[Literal[1], Literal[1]]
+nextafter: ufunc[Literal[2], Literal[1]]
+not_equal: ufunc[Literal[2], Literal[1]]
+positive: ufunc[Literal[1], Literal[1]]
+power: ufunc[Literal[2], Literal[1]]
+rad2deg: ufunc[Literal[1], Literal[1]]
+radians: ufunc[Literal[1], Literal[1]]
+reciprocal: ufunc[Literal[1], Literal[1]]
+remainder: ufunc[Literal[2], Literal[1]]
+right_shift: ufunc[Literal[2], Literal[1]]
+rint: ufunc[Literal[1], Literal[1]]
+sign: ufunc[Literal[1], Literal[1]]
+signbit: ufunc[Literal[1], Literal[1]]
+sin: ufunc[Literal[1], Literal[1]]
+sinh: ufunc[Literal[1], Literal[1]]
+spacing: ufunc[Literal[1], Literal[1]]
+sqrt: ufunc[Literal[1], Literal[1]]
+square: ufunc[Literal[1], Literal[1]]
+subtract: ufunc[Literal[2], Literal[1]]
+tan: ufunc[Literal[1], Literal[1]]
+tanh: ufunc[Literal[1], Literal[1]]
+true_divide: ufunc[Literal[2], Literal[1]]
+trunc: ufunc[Literal[1], Literal[1]]
 
 # TODO(shoyer): remove when the full numpy namespace is defined
 def __getattr__(name: str) -> Any: ...
diff --git a/numpy_ufuncs_plugin.py b/numpy_ufuncs_plugin.py
new file mode 100644
index 0000000..f731ba9
--- /dev/null
+++ b/numpy_ufuncs_plugin.py
@@ -0,0 +1,49 @@
+from mypy.nodes import ARG_POS
+from mypy.plugin import Plugin
+import mypy.types
+from mypy.types import CallableType, LiteralType, TupleType, UnionType
+
+
+def ufunc_call_hook(ctx):
+    nin_arg, nout_arg = ctx.type.args
+    if not isinstance(nin_arg, LiteralType):
+        # Not a literal; we can't make the signature any more precise.
+        return ctx.default_signature
+    if not isinstance(nout_arg, LiteralType):
+        return ctx.default_signature
+    nin, nout = nin_arg.value, nout_arg.value
+
+    # Strip off *args and replace it with the correct number of
+    # positional arguments.
+    arg_kinds = [ARG_POS] * nin + ctx.default_signature.arg_kinds[1:]
+    arg_names = (
+        [f'x{i}' for i in range(nin)] +
+        ctx.default_signature.arg_names[1:]
+    )
+    arg_types = (
+        [ctx.default_signature.arg_types[0]] * nin +
+        ctx.default_signature.arg_types[1:]
+    )
+    ndarray_type, generic_type, _ = ctx.default_signature.ret_type.items
+    scalar_or_ndarray = UnionType([ndarray_type, generic_type])
+    if nout == 1:
+        ret_type = scalar_or_ndarray
+    else:
+        ret_type = TupleType([scalar_or_ndarray] * nout)
+
+    return ctx.default_signature.copy_modified(
+        arg_kinds=arg_kinds,
+        arg_names=arg_names,
+        arg_types=arg_types,
+        ret_type=ret_type,
+    )
+
+
+class UFuncPlugin(Plugin):
+    def get_method_signature_hook(self, method):
+        if method == 'numpy.ufunc.__call__':
+            return ufunc_call_hook
+
+
+def plugin(version):
+    return UFuncPlugin
diff --git a/scripts/find_ufuncs.py b/scripts/find_ufuncs.py
index 49a3fbc..3bb92e0 100644
--- a/scripts/find_ufuncs.py
+++ b/scripts/find_ufuncs.py
@@ -10,7 +10,9 @@ def main():
 
     ufunc_stubs = []
     for ufunc in set(ufuncs):
-        ufunc_stubs.append(f'{ufunc.__name__}: ufunc')
+        ufunc_stubs.append(
+            f'{ufunc.__name__}: ufunc[Literal[{ufunc.nin}], Literal[{ufunc.nout}]]'
+        )
     ufunc_stubs.sort()
 
     for stub in ufunc_stubs:
diff --git a/setup.py b/setup.py
index 235683e..9cdee82 100644
--- a/setup.py
+++ b/setup.py
@@ -20,6 +20,7 @@ def find_stubs(package):
     license='BSD',
     version="0.0.1",
     packages=['numpy-stubs'],
+    py_modules=['numpy_ufuncs_plugin'],
     # PEP 561 requires these
     install_requires=['numpy>=1.14.0'],
     package_data=find_stubs('numpy-stubs'),
diff --git a/tests/fail/ufuncs.py b/tests/fail/ufuncs.py
index 876a562..a4a79ff 100644
--- a/tests/fail/ufuncs.py
+++ b/tests/fail/ufuncs.py
@@ -3,3 +3,4 @@
 np.sin.nin + 'foo'  # E: Unsupported operand types
 np.sin(1, foo='bar')  # E: Unexpected keyword argument
 np.sin(1, extobj=['foo', 'foo', 'foo'])  # E: incompatible type
+np.sin(1, 1)  # E: Too many positional arguments
diff --git a/tests/mypy.ini b/tests/mypy.ini
new file mode 100644
index 0000000..278190b
--- /dev/null
+++ b/tests/mypy.ini
@@ -0,0 +1,2 @@
+[mypy]
+plugins = numpy_ufuncs_plugin
diff --git a/tests/reveal/ufuncs.py b/tests/reveal/ufuncs.py
new file mode 100644
index 0000000..3b3aa55
--- /dev/null
+++ b/tests/reveal/ufuncs.py
@@ -0,0 +1,6 @@
+import numpy as np
+
+reveal_type(np.sin(1))  # E: Union[numpy.ndarray, numpy.generic]
+reveal_type(np.sin([1, 2, 3]))  # E: Union[numpy.ndarray, numpy.generic]
+reveal_type(np.sin.nin)  # E: Literal[1]
+reveal_type(np.sin.nout)  # E: Literal[1]
diff --git a/tests/test_stubs.py b/tests/test_stubs.py
index a90cdf7..299b178 100644
--- a/tests/test_stubs.py
+++ b/tests/test_stubs.py
@@ -9,6 +9,7 @@
 PASS_DIR = os.path.join(TESTS_DIR, "pass")
 FAIL_DIR = os.path.join(TESTS_DIR, "fail")
 REVEAL_DIR = os.path.join(TESTS_DIR, "reveal")
+CONF = os.path.join(TESTS_DIR, "mypy.ini")
 
 
 def get_test_cases(directory):
@@ -38,7 +39,7 @@ def get_test_cases(directory):
 
 @pytest.mark.parametrize("path,py2_arg", get_test_cases(PASS_DIR))
 def test_success(path, py2_arg):
-    stdout, stderr, exitcode = api.run([path] + py2_arg)
+    stdout, stderr, exitcode = api.run([path, "--conf", CONF] + py2_arg)
     assert exitcode == 0, stdout
     assert re.match(
         r'Success: no issues found in \d+ source files?',
@@ -48,7 +49,7 @@ def test_success(path, py2_arg):
 
 @pytest.mark.parametrize("path,py2_arg", get_test_cases(FAIL_DIR))
 def test_fail(path, py2_arg):
-    stdout, stderr, exitcode = api.run([path] + py2_arg)
+    stdout, stderr, exitcode = api.run([path, "--conf", CONF] + py2_arg)
 
     assert exitcode != 0
 
@@ -85,7 +86,7 @@ def test_fail(path, py2_arg):
 
 @pytest.mark.parametrize("path,py2_arg", get_test_cases(REVEAL_DIR))
 def test_reveal(path, py2_arg):
-    stdout, stderr, exitcode = api.run([path] + py2_arg)
+    stdout, stderr, exitcode = api.run([path, "--conf", CONF] + py2_arg)
 
     with open(path) as fin:
         lines = fin.readlines()