Preapproval letter for multifamily w/ contingent rental income?

[Susan Franke]

Mornin' folks. 

I read that its a good idea to get a pre-approval letter to shop around for realtors and so sellers know I'm serious about buying, but how does it work when the approval is contingent on the individual property/proposed rental income? Can I still get that letter?

Background: I'm in the market to buy my first property - a multi-family, 3-4 units, and I will live there for at least a year, per FHA guidelines. My credit is great, but I don't want to drop the cash for a 20% payment on such a building. A large bank ran my credit and loosely approved me for an amount that seems too low to get very far (didn't get an official pre-approval letter), and the broker approved me for an amount nearly double (didn't run my credit but has all my financials). Bank vs. broker - HUGE difference in how they handle rental income.

Much gratitude for any insight you can provide! ~ Susan