I have a similar situation. When I was 18, I was pulled over for a routine traffic stop, and the officer asked to search my car. I worked at the United Way at the time, and told him he could look all he wanted. Somehow, he "found" a plastic bag with 3 marajuana roaches in it in my center console ashtray. The one I had just dumped out at the gas station.
I tried to explain to the cop that he was an idiot for "finding" this evidence, as I had just taken a drug test at work the week before, and was sure a court would question as to why someone who had random drug tests at work would be currently using drugs...
To make a VERY long story short, the court deferred everything, and I pleaded "no contest" to the charges. I was given something called citizen something-or-other and they could call me in for a drug test if they wanted to (they never did). Suffice to say, I am being up front with it on my application, and three of my LOR's are aware of the situation and plan to comment on it in their letters (one is the mayor, the other is a state senator, and the third is a former AF Commaned or NORAD). Plus, it was 7 years ago which I'm sure they will take into account.
Also, in my essay thingy I plan to use it as an indication of my maturation and determination to become a better person since then. I think if I show I'm not afraid of admitting my mistakes, and doing what is important to rectify them and become a better person because of them, it will gain a favorable light in front of the board.