I was able to refi my rental without bringing a dollar to the table. It was originally purchased with an FHA loan, I refinanced through FHA Streamline Refinance. Most mortgage people I spoke to said I had to go through the servicer (wells fargo), but I was able to refi through a local credit union, who then sold/transferred the loan to wells fargo. I received the same interest rate through the credit union that WF offered, but was paid points by the credit union which covered all closing costs and even lowered the principle by ~$600. WF wanted about $5,000 for closing costs for the same loan.