Energy-discriminating, photon counting (EDPC) detectors have been proposed for CT systems for their spectral imaging capabilities, improved dose efficiency and higher spatial resolution. However, these advantages disappear at high flux because of the damaging effects of pulse pileup. From an information theoretic standpoint, spectral information is lost. The information loss is particularly high when we assume that the EDPC detector extracts information using a bank of comparators, as current EDPC detectors do. We analyze the use of alternative pulse detection logic which could preserve information in the presence of pileup. For example, the peak-only detector counts only a single event at the peak energy of multiple pulses which are piled up. We describe and evaluate five of these alternatives in simulation by numerically estimating the Cramer-Rao lower bound of the variance. At high flux, alternative mechanisms outperform comparators. In spectral imaging tasks, the variance reduction can be as high as an order of magnitude.