Put minimum down on primary residence if you have a 20% down payment?

I recently ran across this idea, and wanted to get some input if people have tried this. We have 20% cash for a down payment, don't currently own a house and are looking to purchase. This idea is to make the minimum down payment of 3.5% or 5% (which theoretically gets you a better interest rate), close, then after some time period pay the rest of the 15% cash towards the loan, and then recast the loan and keep the lower interest rate. This strategy seems to assume a few things (interest rate is lower with lower % down, you can recast the loan, no penalties for paying off early, PMI can go away), but if those assumptions work out is this a viable option? Worth the hassle/risk? Thanks