There is probably a program out there for you. I'm getting a 10% down no pmi loan from my credit unions in house financing program. I did quite a bit of hunting around to find this. Non fha 80+%ltv is definitely a big ymmv area. I had wildly different options interest rates and monthly payments between lenders and several flat out nope we can't help yous.
FICO: 782(Ex, AMEX 8/12), Mortgage Pull(3.0%, 5/1 ARM from Local CU 2/2013): 725(EX), 757(TU), 772(EQ); 775(EX, Amex 8/14)
Cards: Amex BCE(10300), Discover(7000), Target (1000), PenFed Platinum Rewards Visa (8500), Chase Freedom(5000), Barclay Arrival+ (10000), Amex HHonors Surpass(11,800)
App'd: Barclay & Hhonors Surpass Aug 2014, PenFed & Freedom Feb 2013, Amex & Target Jul 2012, Discover Feb 2008 Gardening til ???
Goals: TBD, possibly a mortgage refi to a fixed rate or better adjustable