should I tell prospective employer about DUI?

I've had 2 interviews. Having a 3rd next week, I believe they'll make an offer. I did the on-line application for them weeks ago, where I answered "Yes" to have you been convicted of a crime. I gave the misdemeanor code number, date, and court in "Explanation." I thought, if they were going to have a problem with it, they would have seen it then. But I'm beginning to think they don't actually notice until they run the background check. I believe this has already worked against me once (I thought I had an offer, it fell through after background check- again- I admitted "Yes" on all applications and explained the situation.) It was a DUI, early 2002. Nothing since. Should I tell the company about this DUI before I even go ahead with this next interview? Or is admitting it on the Application (and background check when they request)- adequate? My feeling is that they actually don't see it until the background check, and even though you put it on paper- they see it as a surprise.