diff --git a/.travis.yml b/.travis.yml
@@ -51,10 +51,7 @@ matrix:
       env: TESTING=docs
       before_script:
         - cd Doc
-        # Sphinx is pinned so that new versions that introduce new warnings won't suddenly cause build failures.
-        # (Updating the version is fine as long as no warnings are raised by doing so.)
-        # The theme used by the docs is stored separately, so we need to install that as well.
-        - python -m pip install sphinx==1.8.2 blurb python-docs-theme
+        - make venv PYTHON=python
       script:
         - make check suspicious html SPHINXOPTS="-q -W -j4"
     - name: "Documentation tests"

diff --git a/Doc/Makefile b/Doc/Makefile
@@ -143,7 +143,7 @@ clean:
 venv:
 	$(PYTHON) -m venv $(VENVDIR)
 	$(VENVDIR)/bin/python3 -m pip install -U pip setuptools
-	$(VENVDIR)/bin/python3 -m pip install -U Sphinx==2.3.1 blurb python-docs-theme
+	$(VENVDIR)/bin/python3 -m pip install -r requirements.txt
 	@echo "The venv has been created in the $(VENVDIR) directory"
 
 dist:

diff --git a/Doc/requirements.txt b/Doc/requirements.txt
@@ -0,0 +1,12 @@
+# Requirements to build the Python documentation
+
+# Sphinx version is pinned so that new versions that introduce new warnings
+# won't suddenly cause build failures. Updating the version is fine as long
+# as no warnings are raised by doing so.
+sphinx==2.4.4
+
+blurb
+
+# The theme used by the documentation is stored separately, so we need
+# to install that as well.
+python-docs-theme