A supersequence over a finite set is a sequence that contains as subsequence all permutations of the set. This paper defines an infinite array of methods to create supersequences of decreasing lengths. This yields the shortest known supersequences over larger sets. It also provides the best results asymptotically. It is based on a general proof using a new property called strong completeness. The same technique also can be used to prove existing supersequences which combines the old and new ones into an unified conceptual framework.