  Poisson approximation using Stein's method has been extensively studied in
the literature. The main focus has been on bounding the total variation
distance. This paper is a first attempt on moderate deviations in Poisson
approximation for right-tail probabilities of sums of dependent indicators. We
obtain results under certain general conditions for local dependence as well as
for size-bias coupling. These results are then applied to independent
indicators, 2-runs, and the matching problem.
