Let X_1,...,X_n be an i.i.d. sample from a Poisson mixture distribution p(k) = \int_0^\infty s^k e^{-s}f(s) ds/k!. Rates of convergence in Integrated Mean Squared error of orthogonal series estimators for the mixing density f are studied. We derive upper and lower bounds on the IMSE and show, and conclude that our estimator achieves the optimal rate of convergence of order (log n log log n)^r. The analysis further reveals that the considered estimator is automatically adaptive. The analysis of the lower bound is of particular interest: previous analysis have shown that there was a gap between the lower and upper bounds. My analysis eliminates this. It also is applicable to general mixtures of discrete random variables.