An adaptive parallel sorting algorithm is presented, which is cost optimal with respect to the number of oscillations in a sequence (Osc). More specifically, the algorithm sorts any sequence X of length n in time O(log n) by using O(n/log n · log Osc(X)/n) CRCW PRAM processors. This is the first adaptive parallel sorting algorithm that is cost optimal with respect to Osc and, hence, it is also optimal with respect to both the number of inversions (Inv) and the number of runs (Runs) in the sequence. Our result improves previous results on adaptive parallel sorting.