We theoretically investigate the impact of nonlinear dispersion of crystals and multilayers used in Laue-type pulse compressors (LPCs) on chirped x-ray pulse compression, as well as the optimization method for the configuration of LPCs. We also study the application of LPCs to compress chirped x-ray free-electron laser pulses based on the parameters of LCLS-II-HE. The results show that the optimal thickness is half of the Pendellosung period, yielding the best compressor performance with minimal impact from the nonlinear dispersion. This work also provides a new idea for generating ultra-short two-color or multi-color x-ray pulses by considering deviations from the optimized thickness.