A shorthand universal cycle for permutations is a cyclic string in which each shorthand permutation appears exactly once as a unique substring. In this paper, we present three simple and efficient methods of generating shorthand universal cycles for permutations, and these three methods generate a total of 2 + ∏ t = 2 n − 2 t ! shift inequivalent shorthand universal cycles for permutations. In addition, each of the three new methods can be used to generate a shorthand universal cycle for permutations in O ( 1 ) -amortized time per symbol using O ( n ) space.