To get drawn easier...go to the Ranger Station in Leavenworth on a Thursday or Friday Morning right when it opens (6:30 or 7am?). Go up Colchuck or Aasgard. I've never had a problem getting permits for 4 people for the weekend.
Take crampons and ice ax, and go up Colchuck side in early summer. Pictures from Dragon Tail or Prusik are incredible!