Dog will only poop at dog park or hold it and poop in house

Hi,
We got a 1 year old mix from the local humane society in November 2008. Hes a year and a half now and he has literally never pooped on the leash.......ever. He pees on the leash just fine, but no poop. We had to become members of the only local dog park just so that he would poop somewhere. If we don't take him to the park every single day, he poops in the house. So we were wondering if there is anything that anybody could recommend that we do. We would like to avoid crate training, but thats what we have had to do while we are not home. He is the perfect dog in every other way and he always feels bad when he goes in the house because he knows its wrong, but I think its because he just couldn't hold it. This is a really frustrating situation and I would appreciate anybody's help

Thanks