How can I get AWstats to segregate data for two different VirtualHosts/domains?

I want stats for two sites to be displayed separately in their AWstats page on a Debian squeeze VPS.

Right now the two sites have their own *.conf files with separate VirtualHosts, and their VirtualHosts have their own log files (in "combined" format for AWstats). They also have their own config files in /etc/awstats, which reference the two respective log files. However, when I view the pages, they both seem to report the same stats. And I don't expect them to be the same: I believe one site has an order of magnitude more traffic than the other.

Is there anything else I could be requesting so that A sees its own data only and B sees its own data only? Any gotchas with AWstats? The upper-left-hand corner of the AWstats window displays the correct domain name; in other words, they don't both claim to be the site with the heavier traffic. Do I need to move the AWstats alias from the main configuration file to inside respective VirtualHosts?

Thanks,