diff --git a/README.md b/README.md
index f468bbb..4d4de36 100644
--- a/README.md
+++ b/README.md
@@ -166,6 +166,7 @@ dev
 * Python >=3.8 required
 * `Type[...]` dispatches on class arguments
 * `|` syntax for union types
+* `overload` supports generics
 
 1.9.1
 
diff --git a/multimethod/__init__.py b/multimethod/__init__.py
index 7a50b09..eb077c7 100644
--- a/multimethod/__init__.py
+++ b/multimethod/__init__.py
@@ -397,7 +397,7 @@ def __new__(cls, func):
 
     def __init__(self, func: Callable):
         for name, value in get_type_hints(func).items():
-            if not callable(value) or isinstance(value, type):
+            if not callable(value) or isinstance(value, type) or hasattr(value, '__origin__'):
                 func.__annotations__[name] = isa(value)
         self[inspect.signature(func)] = func
 
diff --git a/pyproject.toml b/pyproject.toml
index 6587a74..ab08cb4 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -21,6 +21,7 @@ classifiers = [
     "Programming Language :: Python :: 3.9",
     "Programming Language :: Python :: 3.10",
     "Programming Language :: Python :: 3.11",
+    "Programming Language :: Python :: 3.12",
     "Topic :: Software Development :: Libraries :: Python Modules",
     "Typing :: Typed",
 ]
diff --git a/tests/test_overload.py b/tests/test_overload.py
index 006dba7..0f86581 100644
--- a/tests/test_overload.py
+++ b/tests/test_overload.py
@@ -1,5 +1,5 @@
 import pytest
-from typing import List, Literal
+from typing import List, Literal, Optional
 from multimethod import DispatchError, isa, overload
 
 
@@ -45,3 +45,12 @@ def test_generic():
     assert not pred([0.0])
     assert pred(0.0)
     assert not pred(1.0)
+
+    @overload
+    def func(arg: Optional[str]):
+        return arg
+
+    assert func('') == ''
+    assert func(None) is None
+    with pytest.raises(DispatchError):
+        func(0)