If you from the US would the DUI not also show up in the FAA pilot records search? As you had to notify the FAA of the DUI?
Altough, I have not seen any of the contract jobs ask for more than the FAA no accident / incident letter.
Then you head down to your local police station and get a no criminal record certificate.... If you get a clean one... Your all set nobody will ever ask for anything else in the contract world (read into it... They dont care... Its just ass coverage and a tick in the box)