Fannie Mae has a program called HomePath - which sets less restrictive, "buyer-friendly" guidelines by which lenders must follow when lending money on a Fannie Mae-owned property. Your choice in homes would be limited to Fannie Mae-owned foreclosed properties, however the benefits to using this type of financing are great in my opinion:
HomePath financing offers:
1. Down payments as low as 3%
2. No mortgage insurance
3. No lender requested appraisal
4. Less competition - HomePath offers a 15 day "first look" period when the property is first listed, where investors are not allowed to bid.
5. Often the homes are lightly "rehabbed" to move in ready, with new carpeting, doors, paint, etc.
The caveat is - you'll likely pay a slightly higher interest rate with this financing, however mortgage interest is tax deductible currently, while mortgage insurance is not.
Check out www.Homepath.com for a full list of details and benefits.