diff --git a/pyupgrade.py b/pyupgrade.py
index 79f2bb2..8c9f28c 100644
--- a/pyupgrade.py
+++ b/pyupgrade.py
@@ -57,6 +57,13 @@ _stdlib_parse_format = string.Formatter().parse
 
 _KEYWORDS = frozenset(keyword.kwlist)
 
+_EXPR_NEEDS_PARENS: Tuple[Type[ast.expr], ...] = (
+    ast.Await, ast.BinOp, ast.BoolOp, ast.Compare, ast.GeneratorExp, ast.IfExp,
+    ast.Lambda, ast.UnaryOp,
+)
+if sys.version_info >= (3, 8):  # pragma: no cover (py38+)
+    _EXPR_NEEDS_PARENS += (ast.NamedExpr,)
+
 
 def parse_format(s: str) -> Tuple[DotFormatPart, ...]:
     """Makes the empty string not a special case.  In the stdlib, there's
@@ -1103,7 +1110,6 @@ SIX_CALLS = {
     'u': '{args[0]}',
     'byte2int': '{args[0]}[0]',
     'indexbytes': '{args[0]}[{rest}]',
-    'int2byte': 'bytes(({args[0]},))',
     'iteritems': '{args[0]}.items()',
     'iterkeys': '{args[0]}.keys()',
     'itervalues': '{args[0]}.values()',
@@ -1122,6 +1128,7 @@ SIX_CALLS = {
     'assertRaisesRegex': '{args[0]}.assertRaisesRegex({rest})',
     'assertRegex': '{args[0]}.assertRegex({rest})',
 }
+SIX_INT2BYTE_TMPL = 'bytes(({args[0]},))'
 SIX_B_TMPL = 'b{args[0]}'
 WITH_METACLASS_NO_BASES_TMPL = 'metaclass={args[0]}'
 WITH_METACLASS_BASES_TMPL = '{rest}, metaclass={args[0]}'
@@ -1244,6 +1251,7 @@ class FindPy3Plus(ast.NodeVisitor):
         self.six_add_metaclass: Set[Offset] = set()
         self.six_b: Set[Offset] = set()
         self.six_calls: Dict[Offset, ast.Call] = {}
+        self.six_calls_int2byte: Set[Offset] = set()
         self.six_iter: Dict[Offset, ast.Call] = {}
         self._previous_node: Optional[ast.AST] = None
         self.six_raise_from: Set[Offset] = set()
@@ -1534,8 +1542,18 @@ class FindPy3Plus(ast.NodeVisitor):
             self.six_type_ctx[_ast_to_offset(node.args[1])] = arg
         elif self._is_six(node.func, ('b', 'ensure_binary')):
             self.six_b.add(_ast_to_offset(node))
-        elif self._is_six(node.func, SIX_CALLS) and not _starargs(node):
+        elif (
+                self._is_six(node.func, SIX_CALLS) and
+                node.args and
+                not _starargs(node)
+        ):
             self.six_calls[_ast_to_offset(node)] = node
+        elif (
+                self._is_six(node.func, ('int2byte',)) and
+                node.args and
+                not _starargs(node)
+        ):
+            self.six_calls_int2byte.add(_ast_to_offset(node))
         elif (
                 isinstance(node.func, ast.Name) and
                 node.func.id == 'next' and
@@ -2006,8 +2024,12 @@ def _replace_call(
         end: int,
         args: List[Tuple[int, int]],
         tmpl: str,
+        *,
+        parens: Sequence[int] = (),
 ) -> None:
     arg_strs = [_arg_str(tokens, *arg) for arg in args]
+    for paren in parens:
+        arg_strs[paren] = f'({arg_strs[paren]})'
 
     start_rest = args[0][1] + 1
     while (
@@ -2062,6 +2084,7 @@ def _fix_py3_plus(
             visitor.six_add_metaclass,
             visitor.six_b,
             visitor.six_calls,
+            visitor.six_calls_int2byte,
             visitor.six_iter,
             visitor.six_raise_from,
             visitor.six_reraise,
@@ -2167,7 +2190,14 @@ def _fix_py3_plus(
             call = visitor.six_calls[token.offset]
             assert isinstance(call.func, (ast.Name, ast.Attribute))
             template = _get_tmpl(SIX_CALLS, call.func)
-            _replace_call(tokens, i, end, func_args, template)
+            if isinstance(call.args[0], _EXPR_NEEDS_PARENS):
+                _replace_call(tokens, i, end, func_args, template, parens=(0,))
+            else:
+                _replace_call(tokens, i, end, func_args, template)
+        elif token.offset in visitor.six_calls_int2byte:
+            j = _find_open_paren(tokens, i)
+            func_args, end = _parse_call_args(tokens, j)
+            _replace_call(tokens, i, end, func_args, SIX_INT2BYTE_TMPL)
         elif token.offset in visitor.six_raise_from:
             j = _find_open_paren(tokens, i)
             func_args, end = _parse_call_args(tokens, j)

diff --git a/tests/six_test.py b/tests/six_test.py
index 9ddffd7..bdcb980 100644
--- a/tests/six_test.py
+++ b/tests/six_test.py
@@ -1,3 +1,5 @@
+import sys
+
 import pytest
 
 from pyupgrade import _fix_py3_plus
@@ -42,6 +44,7 @@ from pyupgrade import _fix_py3_plus
             id='relative import might not be six',
         ),
         ('traceback.format_exc(*sys.exc_info())'),
+        pytest.param('six.iteritems()', id='wrong argument count'),
     ),
 )
 def test_fix_six_noop(s):
@@ -382,12 +385,76 @@ def test_fix_six_noop(s):
             'print(next(iter({1:2}.values())))\n',
             id='six.itervalues inside next(...)',
         ),
+        pytest.param(
+            'for _ in six.itervalues({} or y): pass',
+            'for _ in ({} or y).values(): pass',
+            id='needs parenthesizing for BoolOp',
+        ),
+        pytest.param(
+            'for _ in six.itervalues({} | y): pass',
+            'for _ in ({} | y).values(): pass',
+            id='needs parenthesizing for BinOp',
+        ),
+        pytest.param(
+            'six.int2byte(x | y)',
+            'bytes((x | y,))',
+            id='no parenthesize for int2byte BinOP',
+        ),
+        pytest.param(
+            'six.iteritems(+weird_dct)',
+            '(+weird_dct).items()',
+            id='needs parenthesizing for UnaryOp',
+        ),
+        pytest.param(
+            'x = six.get_method_function(lambda: x)',
+            'x = (lambda: x).__func__',
+            id='needs parenthesizing for Lambda',
+        ),
+        pytest.param(
+            'for _ in six.itervalues(x if 1 else y): pass',
+            'for _ in (x if 1 else y).values(): pass',
+            id='needs parenthesizing for IfExp',
+        ),
+        # this one is bogus / impossible, but parenthesize it anyway
+        pytest.param(
+            'six.itervalues(x for x in y)',
+            '(x for x in y).values()',
+            id='needs parentehsizing for GeneratorExp',
+        ),
+        pytest.param(
+            'async def f():\n'
+            '    return six.iteritems(await y)\n',
+            'async def f():\n'
+            '    return (await y).items()\n',
+            id='needs parenthesizing for Await',
+        ),
+        # this one is bogus / impossible, but parenthesize it anyway
+        pytest.param(
+            'six.itervalues(x < y)',
+            '(x < y).values()',
+            id='needs parentehsizing for Compare',
+        ),
     ),
 )
 def test_fix_six(s, expected):
     assert _fix_py3_plus(s, (3,)) == expected
 
 
+@pytest.mark.xfail(sys.version_info < (3, 8), reason='walrus')
+@pytest.mark.parametrize(
+    ('s', 'expected'),
+    (
+        pytest.param(
+            'for _ in six.itervalues(x := y): pass',
+            'for _ in (x := y).values(): pass',
+            id='needs parenthesizing for NamedExpr',
+        ),
+    ),
+)
+def test_fix_six_py38_plus(s, expected):
+    assert _fix_py3_plus(s, (3,)) == expected
+
+
 @pytest.mark.parametrize(
     ('s', 'expected'),
     (

Six call removal breaks logic inside call
before:
```
import six                                                                                                                                                                                                                                     
                                                                                                                                                                                                                                               
result = {}                                                                                                                                                                                                                                    
for leg in six.itervalues(result.get('something') or {}):                                                                                                                                                                                      
    pass
```
after:
```
import six                                                                                                                                                                                                                                     
                                                                                                                                                                                                                                               
result = {}                                                                                                                                                                                                                                    
for leg in result.get('something') or {}.values():                                                                                                                                                                                             
    pass 
```
should:
```
import six                                                                                                                                                                                                                                     
                                                                                                                                                                                                                                               
result = {}                                                                                                                                                                                                                                    
for leg in (result.get('something') or {}).values():                                                                                                                                                                                             
    pass 
tests/six_test.py::test_fix_six_noop[wrong tests/six_test.py::test_fix_six[needs tests/six_test.py::test_fix_six_py38_plus[needs
tests/six_test.py::test_fix_six_noop[x tests/six_test.py::test_fix_six_noop[from tests/six_test.py::test_fix_six_noop[@mydec\nclass tests/six_test.py::test_fix_six_noop[print(six.raise_from(exc, tests/six_test.py::test_fix_six_noop[print(six.b("\xa3"))] tests/six_test.py::test_fix_six_noop[print(six.b( tests/six_test.py::test_fix_six_noop[class tests/six_test.py::test_fix_six_noop[six.reraise(*err)] tests/six_test.py::test_fix_six_noop[six.b(*a)] tests/six_test.py::test_fix_six_noop[six.u(*a)] tests/six_test.py::test_fix_six_noop[@six.add_metaclass(*a)\nclass tests/six_test.py::test_fix_six_noop[(\n tests/six_test.py::test_fix_six_noop[next()] tests/six_test.py::test_fix_six_noop[relative tests/six_test.py::test_fix_six_noop[traceback.format_exc(*sys.exc_info())] tests/six_test.py::test_fix_six[isinstance(s, tests/six_test.py::test_fix_six[weird tests/six_test.py::test_fix_six[issubclass(tp, tests/six_test.py::test_fix_six[STRING_TYPES tests/six_test.py::test_fix_six[from tests/six_test.py::test_fix_six[six.b("123")-b"123"] tests/six_test.py::test_fix_six[six.b(r"123")-br"123"] tests/six_test.py::test_fix_six[six.b("\\x12\\xef")-b"\\x12\\xef"] tests/six_test.py::test_fix_six[six.ensure_binary("foo")-b"foo"] tests/six_test.py::test_fix_six[six.byte2int(b"f")-b"f"[0]] tests/six_test.py::test_fix_six[@six.python_2_unicode_compatible\nclass tests/six_test.py::test_fix_six[@six.python_2_unicode_compatible\n@other_decorator\nclass tests/six_test.py::test_fix_six[six.get_unbound_function(meth)\n-meth\n] tests/six_test.py::test_fix_six[six.indexbytes(bs, tests/six_test.py::test_fix_six[six.assertCountEqual(\n tests/six_test.py::test_fix_six[six.raise_from(exc, tests/six_test.py::test_fix_six[six.reraise(tp, tests/six_test.py::test_fix_six[six.reraise(*sys.exc_info())\n-raise\n] tests/six_test.py::test_fix_six[six.reraise(\n tests/six_test.py::test_fix_six[class tests/six_test.py::test_fix_six[elide tests/six_test.py::test_fix_six[basic tests/six_test.py::test_fix_six[add_metaclass, tests/six_test.py::test_fix_six[six.itervalues] tests/six_test.py::test_fix_six[six.itervalues tests/six_test.py::test_fix_six[no tests/six_test.py::test_fix_base_classes[import tests/six_test.py::test_fix_base_classes[from tests/six_test.py::test_fix_base_classes[class