diff --git a/parso/_compatibility.py b/parso/_compatibility.py
index 35d83cc..58b186f 100644
--- a/parso/_compatibility.py
+++ b/parso/_compatibility.py
@@ -1,7 +1,3 @@
-"""
-To ensure compatibility from Python ``2.7`` - ``3.3``, a module has been
-created. Clearly there is huge need to use conforming syntax.
-"""
 import platform
 
 is_pypy = platform.python_implementation() == 'PyPy'
diff --git a/parso/python/issue_list.txt b/parso/python/issue_list.txt
index 88ca092..4cd9ebf 100644
--- a/parso/python/issue_list.txt
+++ b/parso/python/issue_list.txt
@@ -24,7 +24,6 @@ A list of syntax/indentation errors I've encountered in CPython.
 
     # Just ignore this one, newer versions will not be affected anymore and
     # it's a limit of 2^16 - 1.
-    "too many annotations" # Only python 3.0 - 3.5, 3.6 is not affected.
 
 # Python/ast.c
     # used with_item exprlist expr_stmt
@@ -54,8 +53,8 @@ A list of syntax/indentation errors I've encountered in CPython.
     "iterable unpacking cannot be used in comprehension"  # [*[] for a in [1]]
     "dict unpacking cannot be used in dict comprehension"  # {**{} for a in [1]}
     "Generator expression must be parenthesized if not sole argument"  # foo(x for x in [], b)
-    "positional argument follows keyword argument unpacking" # f(**x, y) >= 3.5
-    "positional argument follows keyword argument"  # f(x=2, y) >= 3.5
+    "positional argument follows keyword argument unpacking" # f(**x, y)
+    "positional argument follows keyword argument"  # f(x=2, y)
     "iterable argument unpacking follows keyword argument unpacking" # foo(**kwargs, *args)
     "lambda cannot contain assignment"  # f(lambda: 1=1)
     "keyword can't be an expression" # f(+x=1)
@@ -167,10 +166,3 @@ A list of syntax/indentation errors I've encountered in CPython.
     E_OVERFLOW: "expression too long"
     E_DECODE: "unknown decode error"
     E_BADSINGLE: "multiple statements found while compiling a single statement"
-
-
-Version specific:
-Python 3.5:
-    'yield' inside async function
-Python 3.4:
-    can use starred expression only as assignment target
diff --git a/test/test_diff_parser.py b/test/test_diff_parser.py
index 6f71e29..3f120bc 100644
--- a/test/test_diff_parser.py
+++ b/test/test_diff_parser.py
@@ -1,7 +1,6 @@
 # -*- coding: utf-8 -*-
 from textwrap import dedent
 import logging
-import sys
 
 import pytest
 
@@ -1267,7 +1266,6 @@ def test_some_weird_removals(differ):
     differ.parse(code1, copies=1)
 
 
-@pytest.mark.skipif(sys.version_info < (3, 5), reason="Async starts working in 3.5")
 def test_async_copy(differ):
     code1 = dedent('''\
         async def main():
diff --git a/test/test_python_errors.py b/test/test_python_errors.py
index 4b57f7c..322c1b8 100644
--- a/test/test_python_errors.py
+++ b/test/test_python_errors.py
@@ -123,10 +123,6 @@ def _get_actual_exception(code):
     elif wanted == 'SyntaxError: assignment to keyword':
         return [wanted, "SyntaxError: can't assign to keyword",
                 'SyntaxError: cannot assign to __debug__'], line_nr
-    elif wanted == 'SyntaxError: can use starred expression only as assignment target':
-        # Python 3.4/3.4 have a bit of a different warning than 3.5/3.6 in
-        # certain places. But in others this error makes sense.
-        return [wanted, "SyntaxError: can't use starred expression here"], line_nr
     elif wanted == 'SyntaxError: f-string: unterminated string':
         wanted = 'SyntaxError: EOL while scanning string literal'
     elif wanted == 'SyntaxError: f-string expression part cannot include a backslash':