In this paper, an alternative model is examined for the distribution arising out of ascertainment. The weighted beta-binomial is suggested for this purpose as it incorporates the variability in the parameter ø of the weighted binomial distribution. The latter distribution has been the model considered by Rao (1965, 1985) and Kocherlakota and Kocherlakota (1990). Techniques for separate families introduced in Kocherlakota and Kocherlakota (1986) are applied to demonstrate that the weighted beta-binomial model is more appropriate in this situation.