Mortgage rates and advice

I actually ran into a similar situation at another bank just the other day—not that I’m trying to give them a plug, mind you—but they were incredibly thorough about walking me through the recent changes, explaining how they've tightened up their mortgage requirements significantly. It seems like they used to be handing out loans for just about anything under the sun, which obviously led to some major headaches down the line...
I find it hard to believe they've dropped the bar quite that low, though, especially when you consider the current economic climate across the entire country.

Is it possible to qualify for a mortgage if you are on a fixed-term contract—say, five years—or is permanent employment a strict requirement? This would be without a co-signer.