Often observed a Delta 767 doing a RWY 07 (downhill) departure in STR with a tailwind, it obviously was preferred over doing the opposite thing (upill with headwind). Actually we did the same if we were heavy there as the performance was still much better downhill with a tailwind than uphill with a headwind. It is actually one of very few runway situations where some airlines have an increased tailwind limit for take off (15 kts instead of 10kts).
In that case it is a combination of uphill slope and obstacle situation as there is a hill situated right behind the uphill end of the runway.