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Photon counting detectors (PCDs) are classically described as being either paralyzable or nonparalyzable. When the PCD is paralyzed, it is no longer sensitive to the detection of additional flux. A recent strategy in PCD design has been to compensate for detector paralysis by embedding specialized paralysis compensation electronics into the application-specific integrated circuit (ASIC). One such compensation mechanism is the pileup trigger, which places an additional energy bin at very high energy that is triggered only during pileup. Another compensation mechanism is the retrigger architecture, which converts a paralyzable PCD into a nonparalyzable PCD. We propose a third mechanism that modifies the retrigger architecture using dedicated secondary counters. We studied the incremental benefit of these three paralysis compensation mechanisms in simulation. We modeled the spectral response using Monte Carlo simulations and then estimated the variance in basis material decomposition of a single pixel using the Cramér-Rao lower bound (CRLB). In the absence of paralysis compensation, noise in basis material images shows sharp increases at moderate flux (near the characteristic count rate) due to contrast inversion and again at high flux. The pileup trigger reduces noise at high flux but does not eliminate contrast inversion. The retrigger architecture eliminates contrast inversion but does not reduce noise at high flux. Our proposed retrigger architecture with dedicated secondary counters reduce noise at both moderate and high flux. [ABSTRACT FROM AUTHOR]