I am not a broker but I did look into what mortgage options there are between 20% and FHA. This is what I found.

These loans are typically not disclosed on a lender website and you have to call in to ask.

These loans are non-conforming and cannot be sold onto the the US govt thru Fannie/Freddie so they bear a higher interest rate

From memory if the 30 yr fixed was 5% and a FHA was 6.5%, the 10% offer was 6% with points.

This information is 6-9 months old