There ARE stated income programs available at 30% down. Your credit score does have to be pretty high though, 800, obviously good enough, I think the min. is 720+. This program was available about a month ago. It's when people have low credit scores, but have $ they run into problems.
For a short example: I had a client with a very successful business, he was renting a home for $7,500/mo. & had 50% to put down on a home, yet his credit score was about 480. The bank said No Way, even with 50% to put down.
If you'd like me to double check with my lender with 30yrs exp, I'd be happy to find out for you if you can get away with not providing tax returns.