  We show, how the classical Berry-Esseen theorem for normal approximation may
be used to derive rates of convergence for random sums of centerd, real-valued
random variables with respect to a certain class of probability metrics,
including the Kolmogorov and the Wasserstein distances. This technique is
applied to several examples, including the approximation by a Laplace
distribution of a geometric sum of centered random variables with finite third
moment, where a concrete Berry-Esseen bound is derived. This bound reduces to a
bound of the supposedly optimal order $\sqrt{p}$ in the i.i.d. case.
