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This article studies random variables whose stop-loss rank falls between a cer'tain risk (assumed to be integer-valued and non-negative, but not necessarily of life-insurance type) and the compound Poisson approximation to this risk. They con-sist of a compound Poisson part to which some independent Bernoulli-type variables are added. Replacing each term in an individual model with such a random variable leads to an approximating model for the total claims on a portfolio of contracts that is computationally almost as attractive as the compound Poisson approximation used in the standard collective model. The resulting stop-loss premiums are much closer to the real values. 1