We present results of Monte Carlo simulations of the Comptonization of photons in a finite spherical Comptonizing cloud. The energy dependence of the arrival times of the Comptonized photons is very different for different input photon spectra. If the delays observed in the high-frequency QPO of Cyg X-2 and GX 5-1 are the result of Comptonization, multi-channel time-delay measurements may constrain the energy of the input photons and thus provide important information on the accretion process in low-mass X-ray binaries.