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The authors describe ways in which dead time can be used to constructively enhance or diminish the effects of point processes that display bunching, according to whether they are signal or noise and demonstrate that the dead-time-modified count mean and variance for an arbitrary doubly stochastic Poisson point process (DSPP) can be obtained from the Laplace transform of the single-fold and joint moment-generating functions for the driving rate process. The dead time is assumed to be small in comparison with the correlation time of the driving process. The theoretical counting efficiency εm and normalized variance εν for shot-noise light with a rectangular impulse response function are shown to depend principally on the dead-time parameter and on the number of primary events in a correlation time of the driving rate process. The theory is in good accord with the experimental values of these quantities for radioluminescence radiation in three transparent materials (fused silica, quartz and glass).