diff --git a/stdlib/2and3/hmac.pyi b/stdlib/2and3/hmac.pyi
index 9be9cf1c8547..830d53ecb5db 100644
--- a/stdlib/2and3/hmac.pyi
+++ b/stdlib/2and3/hmac.pyi
@@ -35,3 +35,6 @@ def compare_digest(a: str, b: str) -> bool: ...
 def compare_digest(a: bytes, b: bytes) -> bool: ...
 @overload
 def compare_digest(a: bytearray, b: bytearray) -> bool: ...
+
+if sys.version_info >= (3, 7):
+    def digest(key: _B, msg: _B, digest: str) -> bytes: ...
diff --git a/stdlib/2and3/locale.pyi b/stdlib/2and3/locale.pyi
index 59ac3c45217c..73ed0c759d7b 100644
--- a/stdlib/2and3/locale.pyi
+++ b/stdlib/2and3/locale.pyi
@@ -94,8 +94,12 @@ def strcoll(string1: _str, string2: _str) -> int: ...
 def strxfrm(string: _str) -> _str: ...
 def format(format: _str, val: Union[float, Decimal], grouping: bool = ...,
            monetary: bool = ...) -> _str: ...
-def format_string(format: _str, val: Sequence[Any],
-                  grouping: bool = ...) -> _str: ...
+if sys.version_info >= (3, 7):
+    def format_string(format: _str, val: Sequence[Any],
+                      grouping: bool = ..., monetary: bool = ...) -> _str: ...
+else:
+    def format_string(format: _str, val: Sequence[Any],
+                      grouping: bool = ...) -> _str: ...
 def currency(val: int, symbol: bool = ..., grouping: bool = ...,
              international: bool = ...) -> _str: ...
 if sys.version_info >= (3, 5):
diff --git a/stdlib/2and3/math.pyi b/stdlib/2and3/math.pyi
index a4fc306f7f52..92ea4ba69ada 100644
--- a/stdlib/2and3/math.pyi
+++ b/stdlib/2and3/math.pyi
@@ -61,6 +61,8 @@ if sys.version_info >= (3, 3):
 def modf(x: float) -> Tuple[float, float]: ...
 def pow(x: float, y: float) -> float: ...
 def radians(x: float) -> float: ...
+if sys.version_info >= (3, 7):
+    def remainder(x: float, y: float) -> float: ...
 def sin(x: float) -> float: ...
 def sinh(x: float) -> float: ...
 def sqrt(x: float) -> float: ...
diff --git a/stdlib/3/http/client.pyi b/stdlib/3/http/client.pyi
index 9cd46574669a..6bf90c9a2204 100644
--- a/stdlib/3/http/client.pyi
+++ b/stdlib/3/http/client.pyi
@@ -125,7 +125,14 @@ else:
                      exc_tb: Optional[types.TracebackType]) -> bool: ...
 
 class HTTPConnection:
-    if sys.version_info >= (3, 4):
+    if sys.version_info >= (3, 7):
+        def __init__(
+            self,
+            host: str, port: Optional[int] = ...,
+            timeout: int = ...,
+            source_address: Optional[Tuple[str, int]] = ..., blocksize: int = ...
+        ) -> None: ...
+    elif sys.version_info >= (3, 4):
         def __init__(
             self,
             host: str, port: Optional[int] = ...,
diff --git a/stdlib/3/http/server.pyi b/stdlib/3/http/server.pyi
index 2f1d0c2a345c..2e610e547135 100644
--- a/stdlib/3/http/server.pyi
+++ b/stdlib/3/http/server.pyi
@@ -1,9 +1,13 @@
 # Stubs for http.server (Python 3.4)
 
+import sys
 from typing import Any, BinaryIO, Dict, List, Mapping, Optional, Tuple, Union
 import socketserver
 import email.message
 
+if sys.version_info >= (3, 7):
+    from builtins import _PathLike
+
 class HTTPServer(socketserver.TCPServer):
     server_name = ...  # type: str
     server_port = ...  # type: int
@@ -53,8 +57,12 @@ class BaseHTTPRequestHandler:
 
 class SimpleHTTPRequestHandler(BaseHTTPRequestHandler):
     extensions_map = ...  # type: Dict[str, str]
-    def __init__(self, request: bytes, client_address: Tuple[str, int],
-                 server: socketserver.BaseServer) -> None: ...
+    if sys.version_info >= (3, 7):
+        def __init__(self, request: bytes, client_address: Tuple[str, int],
+                     server: socketserver.BaseServer, directory: Optional[Union[str, _PathLike[str]]]) -> None: ...
+    else:
+        def __init__(self, request: bytes, client_address: Tuple[str, int],
+                     server: socketserver.BaseServer) -> None: ...
     def do_GET(self) -> None: ...
     def do_HEAD(self) -> None: ...