Looking to finance less than $80k for investment property

[Jason Haynes]

I have a few properties that I'm interested in, which happen to be less than $80k. My current lender is telling me that they can't finance less than $80k (as an investment property) since the ratio of the fees to the amount of loan is too great. Apparently, since the crash, the government made some rules about how much lenders could charge in relation to the total loan amount. (there is some 3% rule). Has anyone had a similar issue or found some workaround? 

I'm thinking about trying to take out a higher loan (if it appraises) and then paying off a chunk after it closes.