diff --git a/stdlib/2and3/mmap.pyi b/stdlib/2and3/mmap.pyi
index f977d82a469b..22d92b19ab0f 100644
--- a/stdlib/2and3/mmap.pyi
+++ b/stdlib/2and3/mmap.pyi
@@ -1,6 +1,7 @@
 import sys
 from typing import (Optional, Sequence, Union, Generic, overload,
                     Iterable, Iterator, Sized, ContextManager, AnyStr)
+from _typeshed import ReadableBuffer
 
 ACCESS_DEFAULT: int
 ACCESS_READ: int
@@ -40,14 +41,20 @@ class _mmap(Generic[AnyStr]):
     else:
         def flush(self, offset: int = ..., size: int = ...) -> int: ...
     def move(self, dest: int, src: int, count: int) -> None: ...
-    def read(self, n: int = ...) -> AnyStr: ...
+    if sys.version_info >= (3, 3):
+        def read(self, n: int = ...) -> AnyStr: ...
+    else:
+        def read(self, n: int) -> AnyStr: ...
     def read_byte(self) -> AnyStr: ...
     def readline(self) -> AnyStr: ...
     def resize(self, newsize: int) -> None: ...
     def seek(self, pos: int, whence: int = ...) -> None: ...
     def size(self) -> int: ...
     def tell(self) -> int: ...
-    def write(self, bytes: AnyStr) -> None: ...
+    if sys.version_info >= (3, 6):
+        def write(self, bytes: AnyStr) -> int: ...
+    else:
+        def write(self, bytes: AnyStr) -> None: ...
     def write_byte(self, byte: AnyStr) -> None: ...
     def __len__(self) -> int: ...
 
@@ -56,7 +63,15 @@ if sys.version_info >= (3,):
         closed: bool
         if sys.version_info >= (3, 8) and sys.platform != "win32":
             def madvise(self, option: int, start: int = ..., length: int = ...) -> None: ...
-        def rfind(self, sub: bytes, start: int = ..., stop: int = ...) -> int: ...
+        if sys.version_info >= (3, 5):
+            def find(self, sub: ReadableBuffer, start: int = ..., stop: int = ...) -> int: ...
+            def rfind(self, sub: ReadableBuffer, start: int = ..., stop: int = ...) -> int: ...
+        else:
+            def rfind(self, sub: bytes, start: int = ..., stop: int = ...) -> int: ...
+        if sys.version_info >= (3, 6):
+            def write(self, bytes: ReadableBuffer) -> int: ...
+        elif sys.version_info >= (3, 5):
+            def write(self, bytes: ReadableBuffer) -> None: ...
         @overload
         def __getitem__(self, index: int) -> int: ...
         @overload