  The accuracy of compound Poisson approximation to the sum
$S=w_1S_1+w_2S_2+...+w_NS_N$ is estimated.
  Here $S_i$ are sums of independent or weakly dependent random variables, and
$w_i$ denote weights. The overall smoothing effect of $S$ on $w_iS_i$ is
estimated by L\' evy concentration function.
