After experiencing some X11-crashes, it turns out that X11 was using the modesetting driver instead of Nouveau. For some reason my Debian configuration was not selecting the driver I needed.
If you inspect your X log-file (usually /var/log/Xorg.0.log) and look for Modeline entries, the log lines will start with modeset(0) if you are using the modeset driver, and with NOUVEAU(0) if you are using the Nouveau driver.