AWStats on Debian: Incomplete statistics on new month

When you install AWStats on Debian, is executed regularly (once every day via cron /etc/cron.d/awstats) in order to build static statistics pages for the current month (in /var/cache/awstats). However, (on my system) this script is executed every day @3:10am. So in each new month the statistics of the last day of the last month are incomplete. I reported this to Debian with a patch included (Debian bug #706487).