  In this paper we present a general method for estimating rates of accidental
coincidence between a pair of single photon detectors operated within their
saturation regimes. By folding the effects of recovery time of both detectors
and the detection circuit into an "effective duty cycle" we are able to
accomodate complex recovery behaviour at high event rates. As an example, we
provide a detailed high-level model for the behaviour of passively quenched
avalanche photodiodes, and demonstrate effective background subtraction at
rates commonly associated with detector saturation. We show that by
post-processing using the updated model, we observe an improvement in
polarization correlation visibility from 88.7% to 96.9% in our experimental
dataset. This technique will be useful in improving the signal-to-noise ratio
in applications which depend on coincidence measurements, especially in
situations where rapid changes in flux may cause detector saturation.
