Good (1965) and Fienberg & Holland (1972, 1973) have addressed the problem of smoothing multinomial frequencies as one of estimation of the probabilities in the traditional multinomial probability model. Suppose the multinomial has t categories and that the corresponding observed frequencies are n1, ..., nt with In, = N. Concerned with the case when at least one of these frequencies is small, as small as 0 or 1, Good ( 1965, p. 23) criticizes the maximum likelihood estimator {nj/N} of the multinomial probabilities {pj}: