Recipients of the analyzed data frequently expect pseudo-continuous, spectrum-like renderings. Constructing these renderings requires assigning values to more parameters than can be determined from the data. From the sloppy model perspective, some parameter combinations, classified as stiff, can be well determined. However, most parameter combinations are classified as sloppy, and their values can vary widely, having negligible or no effect on the quality of the fit of the parameters to the data but having very large effects on the appearance of the rendered distributions. Creating meaningful spectrum-like renderings requires assigning values to these sloppy parameter combinations by using regularization methods. Examination of the parameterizations in a Fourier index domain underlies a regularization method that assigns values to these sloppy parameter combinations in a way that generates a useful pseudo-continuous representation. These plots satisfy a reasonable set of user expectations concerning what information is conveyed and how it is to be interpreted from the representations.