Previous work shows that a combination of the Cornish-Fisher Expansion (CFE) with discrete-event simulation produces accurate and precise estimates of cycle-time quantiles with very little data storage, provided all workstations in the model are operating under the first-in-first-out (FIFO) dispatching rule. The accuracy of the approach degrades, however, as non-FIFO dispatching policies are employed in at least one workstation. This paper proposes the use of a power transformation for use in combination with the CFE to combat these accuracy problems. The suggested approach is detailed, and three methods for selecting the λ parameter of the power transformation are given. The results of a thorough empirical evaluation of each of the three approaches are given, and the advantages and drawbacks of each approach are discussed. Results show that the combination of the CFE with a power transformation generates cycle-time quantile estimates with high accuracy even for non-FIFO systems.