We just got the letter that our private mortgage insurance has been cancelled! This will save us about $750 compared to letting it cancel automatically in a little over a year. We had just reached 20% paid on the loan.
I did the research and wrote a request letter, and we had to arrange for an appraiser to visit the house for a Broker's Price Opinion (BPO). The bank was actually very easy to work with.
The BPO was interesting too - it gave us six "comps" for houses in our area, talked about how our house compares, and even gave a suggested price for if we wanted to sell.
I wouldn't have thought to apply without reading some of the posts here. Thanks everyone for the inspiration!