-RUN cd /tmp/arvados-python-client-* && $pipcmd install .
-RUN if test -d /tmp/schema-salad-* ; then cd /tmp/schema-salad-* && $pipcmd install . ; fi
-RUN if test -d /tmp/cwltool-* ; then cd /tmp/cwltool-* && $pipcmd install . ; fi
-RUN cd /tmp/arvados-cwl-runner-* && $pipcmd install .
+# The build script sets up our build context with all the Python source
+# packages to install.
+COPY . /usr/local/src/
+# Run a-c-r afterward to check for a successful install.
+RUN python3 -m pip install --no-cache-dir /usr/local/src/* && arvados-cwl-runner --version && crunchstat-summary --version