In this article we discuss a number of objectives we consider important for improving graduate training. In addition, we propose several methods by which each objective may be attained. The suggestions are geared toward Francophone universities in Europe (including France, Belgium, and Switzerland) and their particular constraints, but they may prove useful for colleagues in other countries as well. First, we discuss how doctoral students can receive top-quality training in order to acquire the knowledge specfic to the demands of a future university professor and researcher. Next, we develop more general objectives, including the development of a broad view of the discipline and the acquisition of skills such as the ability to write and publish scientific articles. We also emphasize the involvement of graduate students in professional activities and the necessity of developing close contacts with members of the broader scientific community. Finally, we discuss the selection of and the financial support for graduate students.