In a modeling study, determination of the sensitivity of calculated results to variations or uncertainties in input parameters is critical to understanding the results and prioritizing the gathering of additional data. Numerical modeling of mixed-flow systems in karst aquifers used to obtain estimates of spring discharges includes input parameters such as hydraulic conductivities of the formations, recharge distribution, and drain characteristics (e.g., drain conductance and elevation) used to define the location and properties along the inferred conduit system feeding the discharge spring. This paper evaluates the sensitivity of calculated spring discharges to the above input parameters, and also calculates the importance of the input parameters for the flow calculations. In this context, parameter importance is defined as the absolute value of the product of a normalized parameter sensitivity (derivative with respect to the discharge) and a normalized range for the input variables. Parameters that have a large importance for the calculations have large sensitivities and are poorly known (i.e. they have a large normalized range). Parameters that have low importance have low sensitivities or are well known, or both. A ranking of the input parameters by importance can then be used to optimally reduce the uncertainty in the performance measure of the study (i.e. spring discharge) by applying field and laboratory work to reduce the relative range of the most important parameters. The method is demonstrated for an NPL site near St. Louis, Missouri.