"The Compleat Tenant Screening Process: Pre-Screening," by Drew Sygit, is another good article, which overviews the pre-screening process.
I'm not comfortable ruling out people who don't make 3 times the rent and such, though. Some people are simply more frugal than others and can manage well and forever making only 2 times the rent rate. Consider the individual's prior rent payment history, which is often readily available from the prior landlord. Now, if you intend to almost constantly up the rent as much as possible, especially in a "hot" market, 3 times the rent would make sense.