Just did one today as a matter of fact. Sometimes you are limited to folding in 2 months of escrow into the new loan amount. If the veteran was short on his taxes and had an escrow advance to help pay them, the veteran may need to bring some money to closing. There has to be a benefit. Some lenders use the $50 payment savings as a threshhold. You do not want to pile on the points, in fact there are limits on what you can charge on an IRRRL. I never charge them unless it is a fraction of a point [.625 or less] because it usually is not beneficial to them. They go wicked quick. Just be sure that taxes are already paid if they are due within 60 days and get a payment history for the last 12 months. Get the first page of the note & mortgage as well as the HUD, too. It is best to close after the month's payment has been made. It means less interest is capitalized.
Once you do one, you will realize that this is the simplest streamline of them all. Usually, a .5% funding fee which can be financed.