diff --git a/.travis.yml b/.travis.yml
index 69b33d70c5..553a8215d8 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -25,9 +25,11 @@ matrix:
     - python: '3.7'
       env:
         - TOXENV="py37-linux"
-        - BOTO_CONFIG="/dev/null"  # XXX: why is this here?
+      # The following two lines used to be necessary because Travis left files lying around in ~/.aws/,
+      # messing up our tests. Now fixed since https://github.com/travis-ci/travis-ci/issues/7940
+        # - BOTO_CONFIG="/dev/null"
+      #sudo: true
       dist: xenial
-      sudo: true  # XXX: why is this here vs. others?
 
     - python: '3.6'
       env: TOXENV="py36-linux"
diff --git a/README.md b/README.md
index 746ce81d18..a6df9531ad 100644
--- a/README.md
+++ b/README.md
@@ -77,7 +77,7 @@ package:
 
 For alternative modes of installation, see the [documentation].
 
-Gensim is being [continuously tested](https://travis-ci.org/RaRe-Technologies/gensim) under Python 3.5, 3.6, 3.7 and 3.8.
+Gensim is being [continuously tested](https://travis-ci.org/RaRe-Technologies/gensim) under Python 3.6, 3.7 and 3.8.
 Support for Python 2.7 was dropped in gensim 4.0.0 – install gensim 3.8.3 if you must use Python 2.7.
 
 How come gensim is so fast and memory efficient? Isn’t it pure Python, and isn’t Python slow and greedy?
diff --git a/setup.py b/setup.py
index 41b9db4d37..0a24c67b7d 100644
--- a/setup.py
+++ b/setup.py
@@ -20,8 +20,6 @@
 from setuptools import setup, find_packages, Extension
 from setuptools.command.build_ext import build_ext
 
-if sys.version_info[:2] < (3, 5):
-    raise Exception('This version of gensim needs Python 3.5 or later.')
 
 c_extensions = {
     'gensim.models.word2vec_inner': 'gensim/models/word2vec_inner.c',
@@ -380,6 +378,7 @@ def run(self):
     ],
 
     test_suite="gensim.test",
+    python_requires='>=3.5',
     setup_requires=setup_requires,
     install_requires=install_requires,
     tests_require=linux_testenv,