It turns out the Pentagon Papers were supposed to be just a sideline. He also copied documents on US nuclear strategy, which was horrific. He released the Vietnam documents first because he figured if he started with the nuclear docs, nobody would care about the Vietnam stuff.
He gave the nuclear papers to his brother to hide. His brother hid them first in his compost pile, then got worried and moved them to a garbage bag on the edge of the town dump. The next day, men in suits were seen poking metal rods in his compost pile.
Unfortunately, a freak storm washed away that section of the dump. Ellsberg and his brother spent a year opening garbage bags in the area where it all ended up, to no avail. Ellsberg said his wife considered the storm a gift from God, because if the nuclear papers had hit the light of day, he surely would have spent the rest of his life in prison.