diff --git a/stdlib/2and3/hmac.pyi b/stdlib/2and3/hmac.pyi
index 47bbc7ec0..fd550e320 100644
--- a/stdlib/2and3/hmac.pyi
+++ b/stdlib/2and3/hmac.pyi
@@ -1,6 +1,6 @@
 # Stubs for hmac
 
-from typing import Any, Callable, Optional, Union, overload, AnyStr
+from typing import Any, Callable, Optional, Union, overload, AnyStr, overload
 from types import ModuleType
 import sys
 
@@ -11,7 +11,15 @@ _Hash = Any
 
 digest_size: None
 
-if sys.version_info >= (3, 4):
+if sys.version_info >= (3, 8):
+    _DigestMod = Union[str, Callable[[], _Hash], ModuleType]
+    # In reality digestmod has a default value, but the function always throws an error
+    # if the argument is not given, so we pretend it is a required argument.
+    @overload
+    def new(key: _B, msg: Optional[_B], digestmod: _DigestMod) -> HMAC: ...
+    @overload
+    def new(key: _B, *, digestmod: _DigestMod) -> HMAC: ...
+elif sys.version_info >= (3, 4):
     def new(key: _B, msg: Optional[_B] = ...,
             digestmod: Optional[Union[str, Callable[[], _Hash], ModuleType]] = ...) -> HMAC: ...
 else:
diff --git a/tests/stubtest_whitelists/py38.txt b/tests/stubtest_whitelists/py38.txt
index bbdb0a3ac..8f9fef8e2 100644
--- a/tests/stubtest_whitelists/py38.txt
+++ b/tests/stubtest_whitelists/py38.txt
@@ -46,6 +46,7 @@ functools.partialmethod.__get__
 functools.singledispatchmethod.__call__  # A lie to reflect that the descriptor get returns a callable
 gettext.install
 gettext.translation
+hmac.new  # Stub is a white lie; see comments in the stub
 http.client.HTTPSConnection.__init__
 http.cookiejar.DefaultCookiePolicy.__init__
 http.server.SimpleHTTPRequestHandler.__init__
diff --git a/tests/stubtest_whitelists/py39.txt b/tests/stubtest_whitelists/py39.txt
index fd2feb868..41ad9ada2 100644
--- a/tests/stubtest_whitelists/py39.txt
+++ b/tests/stubtest_whitelists/py39.txt
@@ -97,6 +97,7 @@ functools.singledispatchmethod.__call__
 gettext.install
 gettext.translation
 hmac.compare_digest
+hmac.new  # Stub is a white lie; see comments in the stub
 http.client.HTTPSConnection.__init__
 http.cookiejar.DefaultCookiePolicy.__init__
 http.server.SimpleHTTPRequestHandler.__init__