diff --git a/.travis.yml b/.travis.yml
index fc39025d210..779d1207d13 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -29,7 +29,7 @@ env:
     - MAIN_CMD="pytest ${PYTEST_LIST}"
     - SETUP_CMD="${PYTEST_FLAGS} --cov=MDAnalysis"
     - BUILD_CMD="pip install -e package/ && (cd testsuite/ && python setup.py build)"
-    - CONDA_MIN_DEPENDENCIES="mmtf-python biopython networkx cython matplotlib scipy griddataformats hypothesis gsd codecov"
+    - CONDA_MIN_DEPENDENCIES="pip<21.0 mmtf-python biopython networkx cython matplotlib scipy griddataformats hypothesis gsd codecov"
     - CONDA_PY2_DEPENDENCIES="six funcsigs"
     - CONDA_STANDARD_DEPENDENCIES="${CONDA_MIN_DEPENDENCIES} seaborn>=0.7.0 clustalw=2.1 netcdf4==1.3.1 scikit-learn joblib>=0.12 tqdm>=4.43.0"
     - CONDA_DEPENDENCIES="${CONDA_STANDARD_DEPENDENCIES} mock chemfiles"
@@ -77,4 +77,4 @@ install:
 script:
   - cd ${TRAVIS_BUILD_DIR}
   - echo $MAIN_CMD $SETUP_CMD
-  - eval $MAIN_CMD $SETUP_CMD
\ No newline at end of file
+  - eval $MAIN_CMD $SETUP_CMD
diff --git a/package/setup.py b/package/setup.py
index 753f3dd6ab4..3296a8948ed 100755
--- a/package/setup.py
+++ b/package/setup.py
@@ -626,7 +626,7 @@ def long_description(readme):
                         ],
           },
           ext_modules=exts,
-          python_requires=">=2.7,!=3.0,!=3.1,!=3.2,!=3.3,!=3.4,!=3.5",
+          python_requires=">=2.7,!=3.0.*,!=3.1.*,!=3.2.*,!=3.3,!=3.4.*,<3.9",
           # all standard requirements are available through PyPi and
           # typically can be installed without difficulties through setuptools
           setup_requires=[