We consider the classic problem of estimating T, the total number of species in a population, from repeated counts in a simple random sample. We look first at the Chao-Lee estimator: we initially show that such estimator can be obtained by reconciling two estimators of the unobserved probability, and then develop a sequence of improvements culminating in a Dirichlet prior Bayesian reinterpretation of the estimation problem. By means of this, we obtain simultaneous estimates of T, of the normalized interspecies variance $γ^2$ and of the parameter $λ$ of the prior. Several simulations show that our estimation method is more flexible than several known methods we used as comparison; the only limitation, apparently shared by all other methods, seems to be that it cannot deal with the rare cases in which $γ^2 >1$