This study presents a framework that accounts for the uncertainty, relative importance, and relative contribution of uncertain and spatially variable parameters and the influence of statistical model assumptions in problems of infiltration in unsaturated, heterogeneous formations. The relative importance of the saturated hydraulic conductivity Ks, the van Genuchten α, and ¿ parameters was quantified toward the mean pressure head profile and the fluctuations about it. The broad implications of our study for site characterizations efforts are the following. Statistical moments were seen not to be sufficient for producing reliable modeling estimates. Significant information on the detailed shape of the probability distribution is required in order to produce meaningful predictions. When limited data are available, optimum allocation of resources is accomplished by concentrating on Ks. When more extensive sampling can be done, both Ks and ¿ appear to be critical. Total system performance analyses may not provide the most appropriate modeling estimates. The results of the relative importance of the parameters for a specific layer did not coincide with the conclusions drawn from an analysis of the system as a whole.