diff --git a/stubs/openssl-python/OpenSSL/crypto.pyi b/stubs/openssl-python/OpenSSL/crypto.pyi
index 9fcf39938..e38a26f9c 100644
--- a/stubs/openssl-python/OpenSSL/crypto.pyi
+++ b/stubs/openssl-python/OpenSSL/crypto.pyi
@@ -1,5 +1,6 @@
+import sys
 from datetime import datetime
-from typing import Any, Callable, Iterable, List, Optional, Set, Text, Tuple, Union
+from typing import Callable, Iterable, List, Optional, Set, Text, Tuple, Union
 
 from cryptography.hazmat.primitives.asymmetric import dsa, rsa
 
@@ -29,21 +30,26 @@ class _EllipticCurve:
 def get_elliptic_curves() -> Set[_EllipticCurve]: ...
 def get_elliptic_curve(name: str) -> _EllipticCurve: ...
 
+if sys.version_info >= (3, 0):
+    _StrLike = str
+else:
+    _StrLike = Union[str, unicode]
+
 class X509Name:
     def __init__(self, name: X509Name) -> None: ...
-    countryName: Union[str, unicode]
-    stateOrProvinceName: Union[str, unicode]
-    localityName: Union[str, unicode]
-    organizationName: Union[str, unicode]
-    organizationalUnitName: Union[str, unicode]
-    commonName: Union[str, unicode]
-    emailAddress: Union[str, unicode]
-    C: Union[str, unicode]
-    ST: Union[str, unicode]
-    L: Union[str, unicode]
-    O: Union[str, unicode]
-    OU: Union[str, unicode]
-    CN: Union[str, unicode]
+    countryName: _StrLike
+    stateOrProvinceName: _StrLike
+    localityName: _StrLike
+    organizationName: _StrLike
+    organizationalUnitName: _StrLike
+    commonName: _StrLike
+    emailAddress: _StrLike
+    C: _StrLike
+    ST: _StrLike
+    L: _StrLike
+    O: _StrLike
+    OU: _StrLike
+    CN: _StrLike
     def hash(self) -> int: ...
     def der(self) -> bytes: ...
     def get_components(self) -> List[Tuple[str, str]]: ...
@@ -124,7 +130,7 @@ class X509StoreContext:
     def set_store(self, store: X509Store) -> None: ...
     def verify_certificate(self) -> None: ...
 
-def load_certificate(type: int, buffer: Union[str, unicode]) -> X509: ...
+def load_certificate(type: int, buffer: _StrLike) -> X509: ...
 def dump_certificate(type: int, cert: X509) -> bytes: ...
 def dump_publickey(type: int, pkey: PKey) -> bytes: ...
 def dump_privatekey(
@@ -179,13 +185,13 @@ class NetscapeSPKI:
     def get_pubkey(self) -> PKey: ...
     def set_pubkey(self, pkey: PKey) -> None: ...
 
-def load_publickey(type: int, buffer: Union[str, unicode]) -> PKey: ...
+def load_publickey(type: int, buffer: _StrLike) -> PKey: ...
 def load_privatekey(type: int, buffer: bytes, passphrase: Optional[Union[str, Callable[[int], int]]] = ...): ...
 def dump_certificate_request(type: int, req: X509Req): ...
-def load_certificate_request(type, buffer: Union[str, unicode]) -> X509Req: ...
-def sign(pkey: PKey, data: Union[str, unicode], digest: str) -> bytes: ...
-def verify(cert: X509, signature: bytes, data: Union[str, unicode], digest: str) -> None: ...
+def load_certificate_request(type, buffer: _StrLike) -> X509Req: ...
+def sign(pkey: PKey, data: _StrLike, digest: str) -> bytes: ...
+def verify(cert: X509, signature: bytes, data: _StrLike, digest: str) -> None: ...
 def dump_crl(type: int, crl: CRL) -> bytes: ...
-def load_crl(type: int, buffer: Union[str, unicode]) -> CRL: ...
-def load_pkcs7_data(type: int, buffer: Union[str, unicode]) -> PKCS7: ...
-def load_pkcs12(buffer: Union[str, unicode], passphrase: Optional[Union[str, Callable[[int], int]]] = ...) -> PKCS12: ...
+def load_crl(type: int, buffer: _StrLike) -> CRL: ...
+def load_pkcs7_data(type: int, buffer: _StrLike) -> PKCS7: ...
+def load_pkcs12(buffer: _StrLike, passphrase: Optional[Union[str, Callable[[int], int]]] = ...) -> PKCS12: ...