In this paper, utilizing maps between cyclic groups contained in a finite field, two efficient methods for compressing a Tate pairing defined on a supersingular elliptic curve with prime characteristic p and MOV degree 3 are presented. They compress a pairing value from a string of length of 6logp bits to ones of 3logp and 2logp bits, respectively, and an implementation for both the compressed pairings makes use of the codes for the optimized algorithm of the original pairing and no new code is needed. Both the compressed pairings achieve the speed of the original implementation.