We never had to get a permit for DSP.

For DNP there are tricks. You can do your first night in the tent only wilderness campground Igloo (only 7 sites, outhouse, purify water from creek, bear lockers) & that counts as your 1st day in the wilderness, so your second night out can possibly be one of the better units.

Get to the wilderness access center early in the day to plan your itinerary. They are very strict with quotas in specific units.

This interactive map will familiarize you with the park units & their descriptions:
http://www.nps.gov/dena/planyourvisit/map.htm

I like units 6 (Cathedral Mt) , 9 East branch of Tolklat, 10 West branch of Tolkat, 11 Stony Dome & 13 Mt Eielson

I really like the high tundra & river bar travel rather than willows!