diff --git a/stdlib/2/__builtin__.pyi b/stdlib/2/__builtin__.pyi
index 541122b27bc3..e4193c22e906 100644
--- a/stdlib/2/__builtin__.pyi
+++ b/stdlib/2/__builtin__.pyi
@@ -88,11 +88,15 @@ class type(object):
 
 class int(SupportsInt, SupportsFloat, SupportsAbs[int]):
     @overload
-    def __init__(self) -> None: ...
+    def __init__(self, x: SupportsInt = ...) -> None: ...
+    @overload
+    def __init__(self, x: Union[str, unicode, bytearray], base: int = ...) -> None: ...
+
     @overload
-    def __init__(self, x: SupportsInt) -> None: ...
+    def __new__(cls: Type[_T1], x: SupportsInt = ...) -> _T1: ...
     @overload
-    def __init__(self, x: Union[str, unicode, bytearray], base: int = 10) -> None: ...
+    def __new__(cls: Type[_T1], x: Union[str, unicode, bytearray], base: int = ...) -> _T1: ...
+
     def bit_length(self) -> int: ...
 
     def __add__(self, x: int) -> int: ...
@@ -309,7 +313,8 @@ class unicode(basestring, Sequence[unicode]):
     def __hash__(self) -> int: ...
 
 class str(basestring, Sequence[str]):
-    def __init__(self, object: object='') -> None: ...
+    def __init__(self, object: object = ...) -> None: ...
+    def __new__(cls: Type[_T1], object: object = ...) -> _T1: ...
     def capitalize(self) -> str: ...
     def center(self, width: int, fillchar: str = ...) -> str: ...
     def count(self, x: unicode, __start: Optional[int] = ..., __end: Optional[int] = ...) -> int: ...
diff --git a/stdlib/3.4/enum.pyi b/stdlib/3.4/enum.pyi
index a7e0fd686db3..88a675602449 100644
--- a/stdlib/3.4/enum.pyi
+++ b/stdlib/3.4/enum.pyi
@@ -24,8 +24,11 @@ class Enum(metaclass=EnumMeta):
     name = ...  # type: str
     value = ...  # type: Any
 
-class IntEnum(int, Enum):
+_T1 = TypeVar('_T1')
+
+class IntEnum(int, Enum):  # type: ignore
     value = ...  # type: int
+    def __new__(cls: Type[_T1], value: Any) -> _T1: ...
 
 def unique(enumeration: _S) -> _S: ...
 
diff --git a/stdlib/3/builtins.pyi b/stdlib/3/builtins.pyi
index f2a3b1b929c8..5d9ba56df67e 100644
--- a/stdlib/3/builtins.pyi
+++ b/stdlib/3/builtins.pyi
@@ -103,7 +103,16 @@ class super:
     def __init__(self) -> None: ...
 
 class int(SupportsInt, SupportsFloat, SupportsAbs[int]):
-    def __init__(self, x: Union[SupportsInt, str, bytes] = ..., base: int = ...) -> None: ...
+    @overload
+    def __init__(self, x: SupportsInt = ...) -> None: ...
+    @overload
+    def __init__(self, x: Union[str, bytes], base: int = ...) -> None: ...
+
+    @overload
+    def __new__(cls: Type[_T1], x: SupportsInt = ...) -> _T1: ...
+    @overload
+    def __new__(cls: Type[_T1], x: Union[str, bytes], base: int = ...) -> _T1: ...
+
     def bit_length(self) -> int: ...
     def to_bytes(self, length: int, byteorder: str, *, signed: bool = ...) -> bytes: ...
     @classmethod
@@ -227,11 +236,15 @@ class complex(SupportsAbs[float]):
 
 class str(Sequence[str]):
     @overload
-    def __init__(self) -> None: ...
+    def __init__(self, o: object = ...) -> None: ...
     @overload
-    def __init__(self, o: object) -> None: ...
+    def __init__(self, o: bytes, encoding: str = ..., errors: str = ...) -> None: ...
+
+    @overload
+    def __new__(cls: Type[_T1], o: object = ...) -> _T1: ...
     @overload
-    def __init__(self, o: bytes, encoding: str = ..., errors: str = 'strict') -> None: ...
+    def __new__(cls: Type[_T1], o: bytes, encoding: str = ..., errors: str = ...) -> _T1: ...
+
     def capitalize(self) -> str: ...
     def casefold(self) -> str: ...
     def center(self, width: int, fillchar: str = ' ') -> str: ...
diff --git a/third_party/2/enum.pyi b/third_party/2/enum.pyi
index 4032e818b80c..47f89900f8a9 100644
--- a/third_party/2/enum.pyi
+++ b/third_party/2/enum.pyi
@@ -1,4 +1,4 @@
-from typing import List, Any, TypeVar
+from typing import List, Any, TypeVar, Type
 
 class Enum:
     def __new__(cls, value: Any) -> None: ...
@@ -12,8 +12,9 @@ class Enum:
     name = ...  # type: str
     value = ...  # type: Any
 
-class IntEnum(int, Enum): ...
-
 _T = TypeVar('_T')
 
+class IntEnum(int, Enum):  # type: ignore
+    def __new__(cls: Type[_T], value: Any) -> _T: ...
+
 def unique(enumeration: _T) -> _T: ...