diff --git a/python/invoke_release/tasks.py b/python/invoke_release/tasks.py
index e96d57e..5e79a1d 100644
--- a/python/invoke_release/tasks.py
+++ b/python/invoke_release/tasks.py
@@ -3,21 +3,18 @@
 import codecs
 from contextlib import closing
 import datetime
-from distutils.version import LooseVersion
+import importlib
 import json
 import os
-from pkg_resources import parse_version
 import re
 import shlex
 import subprocess
 import sys
 import tempfile
+import urllib.request
 
 from invoke import task
-import six
-from six import moves
-from six.moves import urllib
-from wheel import archive
+from packaging.version import Version, parse as parse_version
 
 RE_CHANGELOG_FILE_HEADER = re.compile(r'^=+$')
 RE_CHANGELOG_VERSION_HEADER = re.compile(r'^-+$')
@@ -143,12 +140,8 @@ def _standard_output(message, *args, **kwargs):
 
 def _prompt(message, *args, **kwargs):
     _print_output(COLOR_WHITE, message + ' ', *args, **kwargs)
-    # noinspection PyCompatibility
-    response = moves.input()
+    response = input()
     if response:
-        if not isinstance(response, six.text_type):
-            # Input returns a bytestring in Python 2 and a unicode string in Python 3
-            return response.decode('utf8').strip()
         return response.strip()
     return ''
 
@@ -329,7 +322,7 @@ def _prompt_for_changelog(verbose):
     if len(built_up_changelog) > 0:
         _verbose_output(verbose, 'Read {} lines of built-up changelog text:', len(built_up_changelog))
         if verbose:
-            _verbose_output(verbose, six.text_type(built_up_changelog))
+            _verbose_output(verbose, str(built_up_changelog))
         _standard_output('There are existing changelog details for this release. You can "edit" the changes, '
                          '"accept" them as-is, delete them and create a "new" changelog message, or "delete" '
                          'them and enter no changelog.')
@@ -1242,9 +1235,9 @@ def branch(_, verbose=False, no_stash=False):
         if branch_version not in tags:
             raise ReleaseFailure('Version number {} not in the list of available tags.'.format(branch_version))
 
-        _v = LooseVersion(branch_version)
-        minor_branch = '.'.join(list(map(six.text_type, _v.version[:2])) + ['x'])
-        major_branch = '.'.join(list(map(six.text_type, _v.version[:1])) + ['x', 'x'])
+        _v = Version(branch_version).release
+        minor_branch = '.'.join(list(map(str, _v[:2])) + ['x'])
+        major_branch = '.'.join(list(map(str, _v[:1])) + ['x', 'x'])
 
         proceed_instruction = _prompt(
             'Using tag {tag}, would you like to create a minor branch for patch versions (branch {minor}, '
@@ -1419,7 +1412,7 @@ def release(_, verbose=False, no_stash=False):
         else:
             version_info = list(map(int, version_info))
         release_version = version_separator.join(
-            filter(None, ['.'.join(map(six.text_type, version_info[:3])), (version_info[3:] or [None])[0]])
+            filter(None, ['.'.join(map(str, version_info[:3])), (version_info[3:] or [None])[0]])
         )  # This must match the code in VERSION_VARIABLE_TEMPLATE at the top of this file
 
         if not (parse_version(release_version) > parse_version(__version__)):
@@ -1586,8 +1579,7 @@ def rollback_release(_, verbose=False, no_stash=False):
                 _standard_output('The commit was not reverted.')
 
             version_module = __import__('{}.version'.format(MODULE_NAME), fromlist=[str('__version__')])
-            # noinspection PyCompatibility
-            moves.reload_module(version_module)
+            importlib.reload(version_module)
             _post_rollback(__version__, version_module.__version__)
 
             _standard_output('Release rollback is complete.')
@@ -1615,6 +1607,17 @@ def wheel(_):
 
     Future possible changes: Upload to the wheel server.
     """
+    # `wheel.archive` was removed in wheel 0.32. On modern environments we
+    # cannot run this task; on older environments (wheel <0.32) it still works.
+    try:
+        from wheel import archive  # noqa: F401  (lazy import on purpose)
+    except ImportError:
+        raise ReleaseFailure(
+            'The `invoke wheel` task requires `wheel<0.32` (the `wheel.archive` '
+            'module was removed in wheel 0.32). Build wheels with '
+            '`python -m build --wheel` instead.'
+        )
+
     build_instruction = _prompt('Build a wheel archive of {}? (Y/n):'.format(MODULE_DISPLAY_NAME)).lower()
 
     if build_instruction == INSTRUCTION_NO:
@@ -1630,11 +1633,10 @@ def wheel(_):
 
 
 def open_pull_request(branch_name, current_branch_name, display_name, version_to_release, github_token):
-    remote = six.text_type(
-        subprocess.check_output(
-            ['git', 'remote', 'get-url', 'origin'],
-            stderr=subprocess.STDOUT,
-        )
+    remote = subprocess.check_output(
+        ['git', 'remote', 'get-url', 'origin'],
+        stderr=subprocess.STDOUT,
+        universal_newlines=True,
     )
     repo = (remote.split(':')[1].split('.')[0])
     url = 'https://api.github.com/repos/{}/pulls'.format(repo)
diff --git a/setup.py b/setup.py
index 1940a5d..d73f631 100644
--- a/setup.py
+++ b/setup.py
@@ -13,9 +13,9 @@
 
 # No dependencies to keep the library lightweight
 install_requires = [
-    'invoke~=0.22.0',
-    'six~=1.11.0',
-    'wheel~=0.31.1'
+    'invoke>=1.0,<3.0',
+    'packaging>=20.0',
+    'wheel>=0.31.1',
 ]
 
 tests_require = [