I always run my group on FFA looting and once my bags are full spend a few seconds trading the stuff to another character (there is a macro in the forums for accepting trades).

This way I never have to touch my other characters until I go back to a town and want to sell up. Of course this doesn't help with quest items but still I ffa loot the corpse and if it's still shining afterwards I know there is a quest item an alt can take.