If you wait until the tower targets a creep, even better if it is a super creep or turret creep, and drop the gun in range of the tower, it can do quite a bit of damage to the tower, especially if there are no enemy minions around... If there are some enemy minions around fighting yours, you can often still position your turret so the tower is the only thing it will be able to hit, so it will focus it anyway. You can also have the turret stay around twice as long (long enough to drop another turret, i usually find) if you use your ult to save it just as it's about to die. You are giving up a turret in your line for this, but you are only doing this when you already have total superiority with minions in the area and your line turrets aren't currently hitting anything anyway, so it's not too bad.
I've also found this tactic surprisingly good at drawing out the enemy champ into a vulnerable position, as they often rush up desperately to kill it like they think it's going to one-shot their tower or something if they don't kill it in that couple of seconds before their tower kills it anyway.