In developing a reliable approach for inferring hydrological properties through inverse modeling of tracer data, decisions made on how to parameterize heterogeneity (i.e., how to represent a heterogeneous distribution using a limited number of parameters that are amenable to estimation) are of paramount importance, as errors in the model structure are partly compensated for by estimating biased property values during the inversion. These biased estimates-while potentially providing an improved fit to the calibration data-may lead to wrong interpretations and conclusions and reduce the ability of the model to make reliable predictions. We consider the estimation of spatial variations in permeability and several other parameters through inverse modeling of tracer data, specifically synthetic and actual field data associated with the 2007 Winchester experiment from the DOE Rifle site. This site represents a challenging setting that reflects the real-world complexities and limitations of dynamic, shallow, alluvial aquifers. Our aim is to highlight and quantify the impact on inversion results of various decisions related to parameterization, such as the positioning of pilot points in a geostatistical parameterization, the handling of upgradient regions, the inclusion of zonal information derived from geophysical data or core logs, extension from 2D to 3D, assumptions regarding the gradient direction, porosity, and the semivariogram function, and deteriorating experimental conditions. This work adds to the relatively limited number of studies that offer guidance on the use of pilot points in complex real-world experiments involving tracer data (as opposed to hydraulic head data).