diff --git a/jedi/api/keywords.py b/jedi/api/keywords.py
index dd57bb85..999e5dc2 100644
--- a/jedi/api/keywords.py
+++ b/jedi/api/keywords.py
@@ -1,18 +1,9 @@
 import pydoc
+from contextlib import suppress
 
-from jedi.inference.utils import ignored
 from jedi.inference.names import AbstractArbitraryName
 
-try:
-    from pydoc_data import topics as pydoc_topics
-except ImportError:
-    # Python 2
-    try:
-        import pydoc_topics
-    except ImportError:
-        # This is for Python 3 embeddable version, which dont have
-        # pydoc_data module in its file python3x.zip.
-        pydoc_topics = None
+from pydoc_data import topics as pydoc_topics
 
 
 class KeywordName(AbstractArbitraryName):
@@ -34,7 +25,7 @@ def imitate_pydoc(string):
     # with unicode strings)
     string = str(string)
     h = pydoc.help
-    with ignored(KeyError):
+    with suppress(KeyError):
         # try to access symbols
         string = h.symbols[string]
         string, _, related = string.partition(' ')
diff --git a/jedi/api/project.py b/jedi/api/project.py
index 08821e30..472507f2 100644
--- a/jedi/api/project.py
+++ b/jedi/api/project.py
@@ -10,7 +10,6 @@ be used across repositories.
 import os
 import errno
 import json
-import sys
 
 from jedi import debug
 from jedi.api.environment import get_cached_default_environment, create_environment
@@ -258,10 +257,6 @@ class Project(object):
         inference_state = s._inference_state
         empty_module_context = s._get_module_context()
 
-        if inference_state.grammar.version_info < (3, 6) or sys.version_info < (3, 6):
-            raise NotImplementedError(
-                "No support for refactorings/search on Python 2/3.5"
-            )
         debug.dbg('Search for string %s, complete=%s', string, complete)
         wanted_type, wanted_names = split_search_string(string)
         name = wanted_names[0]
diff --git a/jedi/inference/arguments.py b/jedi/inference/arguments.py
index 29e7dbeb..99de7210 100644
--- a/jedi/inference/arguments.py
+++ b/jedi/inference/arguments.py
@@ -142,11 +142,8 @@ def unpack_arglist(arglist):
     if arglist is None:
         return
 
-    # Allow testlist here as well for Python2's class inheritance
-    # definitions.
-    if not (arglist.type in ('arglist', 'testlist') or (
-            # in python 3.5 **arg is an argument, not arglist
-            arglist.type == 'argument' and arglist.children[0] in ('*', '**'))):
+    if arglist.type != 'arglist' and not (
+            arglist.type == 'argument' and arglist.children[0] in ('*', '**')):
         yield 0, arglist
         return
 
diff --git a/jedi/inference/compiled/access.py b/jedi/inference/compiled/access.py
index 7c425055..eb2407e7 100644
--- a/jedi/inference/compiled/access.py
+++ b/jedi/inference/compiled/access.py
@@ -8,7 +8,7 @@ import warnings
 import re
 import builtins
 
-from jedi._compatibility import unicode, is_py3, py_version
+from jedi._compatibility import unicode, py_version
 from jedi.inference.compiled.getattr_static import getattr_static
 
 ALLOWED_GETITEM_TYPES = (str, list, tuple, unicode, bytes, bytearray, dict)
@@ -28,17 +28,12 @@ NOT_CLASS_TYPES = (
     types.MethodType,
     types.ModuleType,
     types.TracebackType,
-    MethodDescriptorType
+    MethodDescriptorType,
+    types.MappingProxyType,
+    types.SimpleNamespace,
+    types.DynamicClassAttribute,
 )
 
-if is_py3:
-    NOT_CLASS_TYPES += (
-        types.MappingProxyType,
-        types.SimpleNamespace,
-        types.DynamicClassAttribute,
-    )
-
-
 # Those types don't exist in typing.
 MethodDescriptorType = type(str.replace)
 WrapperDescriptorType = type(set.__iter__)
diff --git a/jedi/inference/gradual/utils.py b/jedi/inference/gradual/utils.py
index f77b5d77..fc68b7b1 100644
--- a/jedi/inference/gradual/utils.py
+++ b/jedi/inference/gradual/utils.py
@@ -14,7 +14,7 @@ def load_proper_stub_module(inference_state, file_io, import_names, module_node)
         # /foo/stdlib/3/os/__init__.pyi -> stdlib/3/os/__init__
         rest = path[len(TYPESHED_PATH) + 1: -4]
         split_paths = tuple(rest.split(os.path.sep))
-        # Remove the stdlib/3 or third_party/3.5 part
+        # Remove the stdlib/3 or third_party/3.6 part
         import_names = split_paths[2:]
         if import_names[-1] == '__init__':
             import_names = import_names[:-1]
diff --git a/jedi/inference/helpers.py b/jedi/inference/helpers.py
index 8f7052d6..7a827d72 100644
--- a/jedi/inference/helpers.py
+++ b/jedi/inference/helpers.py
@@ -12,7 +12,7 @@ from jedi._compatibility import unicode
 
 def is_stdlib_path(path):
     # Python standard library paths look like this:
-    # /usr/lib/python3.5/...
+    # /usr/lib/python3.9/...
     # TODO The implementation below is probably incorrect and not complete.
     if 'dist-packages' in path or 'site-packages' in path:
         return False
diff --git a/jedi/inference/utils.py b/jedi/inference/utils.py
index 17c53577..805aff1d 100644
--- a/jedi/inference/utils.py
+++ b/jedi/inference/utils.py
@@ -99,15 +99,3 @@ class PushBackIterator(object):
         else:
             self.current = next(self.iterator)
         return self.current
-
-
-@contextlib.contextmanager
-def ignored(*exceptions):
-    """
-    Value manager that ignores all of the specified exceptions. This will
-    be in the standard library starting with Python 3.5.
-    """
-    try:
-        yield
-    except exceptions:
-        pass
diff --git a/jedi/inference/value/iterable.py b/jedi/inference/value/iterable.py
index 34b6349d..6d5521fa 100644
--- a/jedi/inference/value/iterable.py
+++ b/jedi/inference/value/iterable.py
@@ -4,7 +4,6 @@ iterators in general.
 """
 import sys
 
-from jedi._compatibility import is_py3
 from jedi.inference import compiled
 from jedi.inference import analysis
 from jedi.inference.lazy_value import LazyKnownValue, LazyKnownValues, \
diff --git a/test/completion/stdlib.py b/test/completion/stdlib.py
index fc8f0f14..1b06d6ca 100644
--- a/test/completion/stdlib.py
+++ b/test/completion/stdlib.py
@@ -133,48 +133,6 @@ weakref.ref(1)
 #? int() None
 weakref.ref(1)()
 
-# -----------------
-# functools
-# -----------------
-import functools
-
-basetwo = functools.partial(int, base=2)
-#? int()
-basetwo()
-
-def function(a, b):
-    return a, b
-a = functools.partial(function, 0)
-
-#? int()
-a('')[0]
-#? str()
-a('')[1]
-
-kw = functools.partial(function, b=1.0)
-tup = kw(1)
-#? int()
-tup[0]
-#? float()
-tup[1]
-
-def my_decorator(f):
-    @functools.wraps(f)
-    def wrapper(*args, **kwds):
-        return f(*args, **kwds)
-    return wrapper
-
-@my_decorator
-def example(a):
-    return a
-
-#? str()
-example('')
-
-# From GH #1574
-#? float()
-functools.wraps(functools.partial(str, 1))(lambda: 1.0)()
-
 # -----------------
 # sqlite3 (#84)
 # -----------------
@@ -386,8 +344,47 @@ X().name
 X().attr_x.attr_y.value
 
 # -----------------
-# functools Python 3.5+
+# functools
 # -----------------
+import functools
+
+basetwo = functools.partial(int, base=2)
+#? int()
+basetwo()
+
+def function(a, b):
+    return a, b
+a = functools.partial(function, 0)
+
+#? int()
+a('')[0]
+#? str()
+a('')[1]
+
+kw = functools.partial(function, b=1.0)
+tup = kw(1)
+#? int()
+tup[0]
+#? float()
+tup[1]
+
+def my_decorator(f):
+    @functools.wraps(f)
+    def wrapper(*args, **kwds):
+        return f(*args, **kwds)
+    return wrapper
+
+@my_decorator
+def example(a):
+    return a
+
+#? str()
+example('')
+
+# From GH #1574
+#? float()
+functools.wraps(functools.partial(str, 1))(lambda: 1.0)()
+
 class X:
     def function(self, a, b):
         return a, b
@@ -440,11 +437,6 @@ X().just_partial('')[0]
 #? str()
 X().just_partial('')[1]
 
-
-# -----------------
-# functools Python 3.8
-# -----------------
-
 # python >= 3.8
 
 @functools.lru_cache