diff --git a/stdlib/@tests/stubtest_allowlists/common.txt b/stdlib/@tests/stubtest_allowlists/common.txt
index 13024e94a..f29461ebc 100644
--- a/stdlib/@tests/stubtest_allowlists/common.txt
+++ b/stdlib/@tests/stubtest_allowlists/common.txt
@@ -417,8 +417,6 @@ csv.DictWriter.__init__  # runtime sig has *args but will error if more than 5 p
 dataclasses.field  # White lies around defaults
 email.policy.EmailPolicy.message_factory  # "type" at runtime, but protocol in stubs
 hashlib.scrypt  # Raises TypeError if salt, n, r or p are None
-hashlib.sha3_\d+  # Can be a class or a built-in function, can't be subclassed at runtime
-hashlib.shake_\d+  # Can be a class or a built-in function, can't be subclassed at runtime
 hmac.HMAC.blocksize  # use block_size instead
 
 # We can't distinguish not having a default value from having a default value of inspect.Parameter.empty
diff --git a/stdlib/@tests/stubtest_allowlists/py38.txt b/stdlib/@tests/stubtest_allowlists/py38.txt
index 8a8cebab1..ace9fd787 100644
--- a/stdlib/@tests/stubtest_allowlists/py38.txt
+++ b/stdlib/@tests/stubtest_allowlists/py38.txt
@@ -262,3 +262,7 @@ email._header_value_parser.SPECIALSNL
 email.errors.HeaderWriteError
 email.utils.getaddresses
 email.utils.parseaddr
+
+# Weird special builtins that are typed as functions, but aren't functions
+hashlib.sha3_\d+  # Class in 3.8, can't be subclassed at runtime, built-in function 3.9+
+hashlib.shake_\d+  # Class in 3.8, can't be subclassed at runtime, built-in function 3.9+
diff --git a/stdlib/hashlib.pyi b/stdlib/hashlib.pyi
index 059f0f6e4..74687d9ab 100644
--- a/stdlib/hashlib.pyi
+++ b/stdlib/hashlib.pyi
@@ -56,12 +56,20 @@ class _Hash:
     def block_size(self) -> int: ...
     @property
     def name(self) -> str: ...
-    def __init__(self, data: ReadableBuffer = ...) -> None: ...
     def copy(self) -> Self: ...
     def digest(self) -> bytes: ...
     def hexdigest(self) -> str: ...
     def update(self, data: ReadableBuffer, /) -> None: ...
 
+class _VarLenHash:
+    digest_size: int
+    block_size: int
+    name: str
+    def copy(self) -> _VarLenHash: ...
+    def digest(self, length: int, /) -> bytes: ...
+    def hexdigest(self, length: int, /) -> str: ...
+    def update(self, data: ReadableBuffer, /) -> None: ...
+
 if sys.version_info >= (3, 9):
     def new(name: str, data: ReadableBuffer = b"", *, usedforsecurity: bool = ...) -> _Hash: ...
     def md5(string: ReadableBuffer = b"", *, usedforsecurity: bool = True) -> _Hash: ...
@@ -70,6 +78,12 @@ if sys.version_info >= (3, 9):
     def sha256(string: ReadableBuffer = b"", *, usedforsecurity: bool = True) -> _Hash: ...
     def sha384(string: ReadableBuffer = b"", *, usedforsecurity: bool = True) -> _Hash: ...
     def sha512(string: ReadableBuffer = b"", *, usedforsecurity: bool = True) -> _Hash: ...
+    def sha3_224(string: ReadableBuffer = b"", *, usedforsecurity: bool = True) -> _Hash: ...
+    def sha3_256(string: ReadableBuffer = b"", *, usedforsecurity: bool = True) -> _Hash: ...
+    def sha3_384(string: ReadableBuffer = b"", *, usedforsecurity: bool = True) -> _Hash: ...
+    def sha3_512(string: ReadableBuffer = b"", *, usedforsecurity: bool = True) -> _Hash: ...
+    def shake_128(string: ReadableBuffer = b"", *, usedforsecurity: bool = True) -> _VarLenHash: ...
+    def shake_256(string: ReadableBuffer = b"", *, usedforsecurity: bool = True) -> _VarLenHash: ...
 
 else:
     def new(name: str, data: ReadableBuffer = b"") -> _Hash: ...
@@ -79,6 +93,12 @@ else:
     def sha256(string: ReadableBuffer = b"") -> _Hash: ...
     def sha384(string: ReadableBuffer = b"") -> _Hash: ...
     def sha512(string: ReadableBuffer = b"") -> _Hash: ...
+    def sha3_224(string: ReadableBuffer = b"") -> _Hash: ...
+    def sha3_256(string: ReadableBuffer = b"") -> _Hash: ...
+    def sha3_384(string: ReadableBuffer = b"") -> _Hash: ...
+    def sha3_512(string: ReadableBuffer = b"") -> _Hash: ...
+    def shake_128(string: ReadableBuffer = b"") -> _VarLenHash: ...
+    def shake_256(string: ReadableBuffer = b"") -> _VarLenHash: ...
 
 algorithms_guaranteed: AbstractSet[str]
 algorithms_available: AbstractSet[str]
@@ -86,24 +106,6 @@ algorithms_available: AbstractSet[str]
 def pbkdf2_hmac(
     hash_name: str, password: ReadableBuffer, salt: ReadableBuffer, iterations: int, dklen: int | None = None
 ) -> bytes: ...
-
-class _VarLenHash:
-    digest_size: int
-    block_size: int
-    name: str
-    def __init__(self, data: ReadableBuffer = ...) -> None: ...
-    def copy(self) -> _VarLenHash: ...
-    def digest(self, length: int, /) -> bytes: ...
-    def hexdigest(self, length: int, /) -> str: ...
-    def update(self, data: ReadableBuffer, /) -> None: ...
-
-sha3_224 = _Hash
-sha3_256 = _Hash
-sha3_384 = _Hash
-sha3_512 = _Hash
-shake_128 = _VarLenHash
-shake_256 = _VarLenHash
-
 def scrypt(
     password: ReadableBuffer, *, salt: ReadableBuffer, n: int, r: int, p: int, maxmem: int = 0, dklen: int = 64
 ) -> bytes: ...