diff --git a/.travis.yml b/.travis.yml
index c207bd7..4e8be5e 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -36,7 +36,7 @@
         # (Updating the version is fine as long as no warnings are raised by doing so.)
         - python -m pip install sphinx~=1.6.1 blurb
       script:
-        - make check suspicious html SPHINXOPTS="-q -W -j4"
+        - make check suspicious html SPHINXBUILD="sphinx-build" SPHINXOPTS="-q -W -j4"
     - os: linux
       language: c
       compiler: gcc
diff --git a/Doc/Makefile b/Doc/Makefile
index 307d1e0..69e7e2e 100644
--- a/Doc/Makefile
+++ b/Doc/Makefile
@@ -17,7 +17,7 @@
 
 .PHONY: help build html htmlhelp latex text changes linkcheck \
 	suspicious coverage doctest pydoc-topics htmlview clean dist check serve \
-	autobuild-dev autobuild-stable venv
+	autobuild-dev autobuild-stable
 
 help:
 	@echo "Please use \`make <target>' where <target> is one of"
@@ -39,7 +39,7 @@
 	@echo "  check      to run a check for frequent markup errors"
 	@echo "  serve      to serve the documentation on the localhost (8000)"
 
-build:
+build: venv
 	-mkdir -p build
 # Look first for a Misc/NEWS file (building from a source release tarball
 # or old repo) and use that, otherwise look for a Misc/NEWS.d directory
@@ -122,9 +122,11 @@
 	-rm -rf build/* $(VENVDIR)/*
 
 venv:
-	$(PYTHON) -m venv $(VENVDIR)
-	$(VENVDIR)/bin/python3 -m pip install -U Sphinx blurb
-	@echo "The venv has been created in the $(VENVDIR) directory"
+	@if [ "$(SPHINXBUILD)" == "PATH=$(VENVDIR)/bin:$$PATH sphinx-build" ]; then \
+		$(PYTHON) -m venv $(VENVDIR); \
+		echo "A virtual environment for Docs has been made in the $(VENVDIR) directory"; \
+		$(VENVDIR)/bin/python3 -m pip install Sphinx blurb; \
+	fi
 
 dist:
 	rm -rf dist
diff --git a/Doc/README.rst b/Doc/README.rst
index a29d1f3..c0a8d89 100644
--- a/Doc/README.rst
+++ b/Doc/README.rst
@@ -21,21 +21,16 @@
 * `Sphinx <https://pypi.org/project/Sphinx/>`_
 * `blurb <https://pypi.org/project/blurb/>`_
 
-The easiest way to install these tools is to create a virtual environment and
-install the tools into there.
+You could manually create a virtual environment and install them, but there is
+a ``Makefile`` already set up to do this for you, as long as you have a working
+Python 3 interpreter available.
 
 
 Using make
 ----------
 
-To get started on UNIX, you can create a virtual environment with the command ::
-
-  make venv
-
-That will install all the tools necessary to build the documentation. Assuming
-the virtual environment was created in the ``env`` directory (the default;
-configurable with the VENVDIR variable), you can run the following command to
-build the HTML output files::
+A Makefile has been prepared so that (on Unix), after you change into the
+``Doc/`` directory you can simply run ::
 
   make html
 
@@ -44,8 +39,17 @@
 (configurable with the SPHINXBUILD and BLURB variables).
 
 On Windows, we try to emulate the Makefile as closely as possible with a
-``make.bat`` file. If you need to specify the Python interpreter to use,
-set the PYTHON environment variable instead.
+``make.bat`` file.
+
+To use a Python interpreter that's not called ``python3``, use the standard
+way to set Makefile variables, using e.g. ::
+
+   make html PYTHON=python
+
+On Windows, set the PYTHON environment variable instead.
+
+To use a specific sphinx-build (something other than ``sphinx-build``), set
+the SPHINXBUILD variable.
 
 Available make targets are:
 
@@ -104,11 +108,14 @@
 Without make
 ------------
 
-First, install the tool dependencies from PyPI.
+Install the Sphinx package and its dependencies from PyPI. In this situation,
+you'll have to create a virtual environment manually, and install Sphinx into
+it. Change into the ``Doc`` directory and run ::
 
-Then, from the ``Doc`` directory, run ::
-
-   sphinx-build -b<builder> . build/<builder>
+   $ python3 -m venv venv
+   $ source venv/bin/activate
+   (venv) $ pip install Sphinx
+   (venv) $ sphinx-build -b<builder> . build/<builder>
 
 where ``<builder>`` is one of html, text, latex, or htmlhelp (for explanations
 see the make targets above).