diff --git a/stdlib/hmac.pyi b/stdlib/hmac.pyi
index b9a867f7b..ee8af1b48 100644
--- a/stdlib/hmac.pyi
+++ b/stdlib/hmac.pyi
@@ -30,7 +30,13 @@ class HMAC:
     block_size: int
     @property
     def name(self) -> str: ...
-    def __init__(self, key: bytes | bytearray, msg: ReadableBuffer | None = None, digestmod: _DigestMod = "") -> None: ...
+    if sys.version_info >= (3, 8):
+        def __init__(self, key: bytes | bytearray, msg: ReadableBuffer | None = None, digestmod: _DigestMod = "") -> None: ...
+    else:
+        def __init__(
+            self, key: bytes | bytearray, msg: ReadableBuffer | None = None, digestmod: _DigestMod | None = None
+        ) -> None: ...
+
     def update(self, msg: ReadableBuffer) -> None: ...
     def digest(self) -> bytes: ...
     def hexdigest(self) -> str: ...
diff --git a/tests/stubtest_allowlists/py37.txt b/tests/stubtest_allowlists/py37.txt
index 3c9a5357e..f83cd84b6 100644
--- a/tests/stubtest_allowlists/py37.txt
+++ b/tests/stubtest_allowlists/py37.txt
@@ -32,7 +32,6 @@ dummy_threading.Condition.release
 dummy_threading.Event.isSet
 dummy_threading.local.__new__
 fractions.Fraction.__new__  # overload is too complicated for stubtest to resolve
-hmac.HMAC.__init__
 inspect.Signature.from_builtin  # Removed in 3.11, can add if someone needs this
 inspect.Signature.from_function  # Removed in 3.11, can add if someone needs this
 ipaddress._BaseNetwork.__init__