diff --git a/stdlib/2/os/__init__.pyi b/stdlib/2/os/__init__.pyi
index 8dad31d6b..3951ba6c9 100644
--- a/stdlib/2/os/__init__.pyi
+++ b/stdlib/2/os/__init__.pyi
@@ -3,6 +3,7 @@
 
 from builtins import OSError as error
 from io import TextIOWrapper as _TextIOWrapper
+from posix import stat_result as stat_result  # TODO: use this, see https://github.com/python/mypy/issues/3078
 import sys
 from typing import (
     Mapping, MutableMapping, Dict, List, Any, Tuple, Iterator, overload, Union, AnyStr,
@@ -126,6 +127,7 @@ _StatVFS = NamedTuple('_StatVFS', [('f_bsize', int), ('f_frsize', int), ('f_bloc
                                    ('f_bfree', int), ('f_bavail', int), ('f_files', int),
                                    ('f_ffree', int), ('f_favail', int), ('f_flag', int),
                                    ('f_namemax', int)])
+
 def ctermid() -> str: ...  # Unix only
 def getegid() -> int: ...  # Unix only
 def geteuid() -> int: ...  # Unix only
diff --git a/stdlib/2and3/traceback.pyi b/stdlib/2and3/traceback.pyi
index 211390992..d53adfe9e 100644
--- a/stdlib/2and3/traceback.pyi
+++ b/stdlib/2and3/traceback.pyi
@@ -1,6 +1,6 @@
 # Stubs for traceback
 
-from typing import Generator, IO, Iterator, List, Mapping, Optional, Tuple, Type
+from typing import Any, Dict, Generator, IO, Iterator, List, Mapping, Optional, Tuple, Type
 from types import FrameType, TracebackType
 import sys
 
@@ -92,10 +92,19 @@ if sys.version_info >= (3, 5):
 
 if sys.version_info >= (3, 5):
     class FrameSummary:
+        filename: str
+        lineno: int
+        name: str
+        line: str
+        locals: Optional[Dict[str, str]]
         def __init__(self, filename: str, lineno: int, name: str,
                      lookup_line: bool = ...,
                      locals: Optional[Mapping[str, str]] = ...,
                      line: Optional[int] = ...) -> None: ...
+        # TODO: more precise typing for __getitem__ and __iter__,
+        # for a namedtuple-like view on (filename, lineno, name, str).
+        def __getitem__(self, i: int) -> Any: ...
+        def __iter__(self) -> Iterator[Any]: ...
 
     class StackSummary(List[FrameSummary]):
         @classmethod
@@ -105,3 +114,4 @@ if sys.version_info >= (3, 5):
                     capture_locals: bool = ...) -> StackSummary: ...
         @classmethod
         def from_list(cls, a_list: List[_PT]) -> StackSummary: ...
+        def format(self) -> List[str]: ...
diff --git a/stdlib/3/builtins.pyi b/stdlib/3/builtins.pyi
index c3cda6d87..80fc8e509 100644
--- a/stdlib/3/builtins.pyi
+++ b/stdlib/3/builtins.pyi
@@ -50,7 +50,7 @@ class object:
     def __sizeof__(self) -> int: ...
     def __reduce__(self) -> tuple: ...
     def __reduce_ex__(self, protocol: int) -> tuple: ...
-    def __dir__(self) -> List[str]: ...
+    def __dir__(self) -> Iterable[str]: ...
 
     if sys.version_info >= (3, 6):
         def __init_subclass__(cls) -> None: ...
diff --git a/stdlib/3/unittest/__init__.pyi b/stdlib/3/unittest/__init__.pyi
index f21bc5f13..6c0e409d9 100644
--- a/stdlib/3/unittest/__init__.pyi
+++ b/stdlib/3/unittest/__init__.pyi
@@ -11,7 +11,7 @@ from types import ModuleType, TracebackType
 
 
 _T = TypeVar('_T')
-_FT = TypeVar('_FT', bound=Callable[[Any], Any])
+_FT = TypeVar('_FT', bound=Callable[..., Any])
 _E = TypeVar('_E', bound=Exception)