The four worst teams get to pick 3-6, in order, and the remaining 10 teams have an equal chance at the reamaining picks. Each team has one ball, and they are pulled in reverse order. Drama.
This ensures that the really bad team get to start building a foundation with a solid lottery pick, and that the somewhat bad teams have a real chance to make a leap. Plus, it gets former college stars into the paloffs sooner (by keeping them off the truly terrible squads), which would benefit the league.
This method eliminates tanking, period. Really bad teams will fight for the number five spot in order to have a chance at the top pick, and fringe playoff teams will not tank for a 10% chance at number one pick.