Estimating stein's constants for compound Poisson approximation

Stein's method for compound Poisson approximation was introduced by Barbour, Chen and Loh. One difficulty in applying the method is that the bounds on the solutions of the Stein equation are by no means as good as for Poisson approximation. We show that, for the Kolmogorov metric and under a condition on the parameters of the approximating compound Poisson distribution, bounds comparable with those obtained for the Poisson distribution can be recovered.