I have started documenting a Python project using Sphinx. It is the first time I use it - I am used to tools which work with a JavaDoc-like syntax, and I have some doubts.
I found this autopackage script from a comment here. It generates the necessary .rst files according to the structure of your packages.
side note: I still feel I am missing something, as I cannot believe that a tool like Sphinx, which is renowned as the most advanced tool for documenting Python, misses the functionality to do basic API documentation. Hence I will leave the question open for a while before accepting my own answer.