OK, this was actually, in many ways quite easy. Though perhaps a mite dangerous...

In my case the mailman is also the supply guy. So I just waited until he brought in the mail to sort and then requested a vital missing computer part. I was sure that he would ask me to come back after he was finished and was prepared to lie in great detail about the relative importance of the vital missing part, but to my amazment, he just said "sure, hang on a sec" and went into the back to find my vital gear. As he began searching through boxes and boxes of supplies, a small line began to grow behind me filled with soldiers, sailors, and marines anxious to receive their mail. As the search contintued and the line grew, I began to notice a change in mood in the mob behind me. I tried to yell "Never mind! I'll come back later" but it was clear my voice was lost in the vastness of the supply room. The mob shifted their feet. The mob sighed loudly. The mob began to mutter. Just as the mob began to rumble in unison, the supply seargant returned - without the vital part. He then explained to me exactly what I would need to do to retrieve the part, which involved coming back after the mail call and filling out several forms in triplicate. This lengthy technical description did nothing to assuage the mood of the mob which began chanting "Mail! Mail! Mail" menacingly. I quickly grabbed the forms and ran for my life.

Total distraction time: 7 minutes.