The current instructions say to run pip install -i https://testpypi.python.org/pypi PACKAGENAME, which is what TestPyPI says to do as well. However, this fails if any dependencies of your package are not on TestPyPI, but only on PyPI.

You can look for dependencies on both regular PyPI and TestPyPI using
pip install PACKAGENAME --extra-index-url=https://test.pypi.org/simple/