Treating endogeneity and flexibility in such a way that efficiency is not sacrified has become a rising point of interest in count data models. We use a polynomial expansion of a Poisson baseline density to compute the full information maximum likelihood (FIML) estimator. In order to test the model we propose measures of goodness of fit, information criteria, likelihood ratio and scores tests for evaluation. We also show how to compute statistics for sensitivity analysis. Then, we test our model using data on number of trips by households and number of physician office visits, finding that low order polynomials may be enough to improve fit significantly.We benefitted from financial support of the Comissionat per a Universitats i Recerca de la Generalitat de Catalunya grant no. 1997FI-436, Universitat Autònoma de Barcelona AP92-34967274 and from Spanish Ministry of Education DGICYT PB96-1160.