older dog was a stray, urinates in my house

I have a Jack Russell that I picked up as a stray about one year ago. He had lost much of his hair, was extemely thin, and had a serious limp. He is now healthy and so precious to me...I adore him. However, he still urinates in my house. Not all the time, but rather frequently. I crate him when I'm going to be gone for any length of time, and this has helped somewhat, but I still find areas where he has urinated. I do not punish him in any way for I never can catch him in the act, and I have no idea when he does this. When I picked him up he was an intact male. I took him to the vet and posted in the newspaper and pet shops in the area, but no one claimed him, so I then had him neutered. The vet estimated that he was probably about 4 years old at the time which means he would be about 5 now. Is there any hope to break him of this. It is very distressing to me. I love him dearly, but I take pride in my home as well, and I'm tired of finding (and smelling!) urine. Is there anything I can do to break him of this? Please help me.