Refinance after rehab

[Scott Meredith]

I just finished a rehab on my personal residence that will become a rental; I added two bedrooms and a bath. My question is I got the final inspection done yesterday and was wondering how long I have to wait before I can refinance conventionally. I know that municipalities (specifically Los Angeles City) don't move quickly, and in fact the inspector said I would get some documentation in the mail in 4-6 weeks. What has been everyone else's experience in getting a lender to lend on my property now as a 4/2 instead of a 2/1? Would showing them the final inspection being completed work, or do I have to wait for the final documentation to come in the mail?