White dwarfs are the end product of evolution for around 98% of the stars in our Galaxy. Buried in their interiors are the records of physical processes that take place during earlier stages in the life of the star. In recent years, a well-established theory of non-radial oscillations, improved white dwarf models, year of expertise built up in the field of white dwarf asteroseismic fitting, and computing power have culminated in the asteroseismology finally delivering what it promised: a detailed map of the interior structure of white dwarfs. As always in science, new results raise new questions. We perform a number of numerical experiments to better understand the connection between a given set of periods varying in the number of periods and in the set of radial overtones and the quality of the constraints on interior structure one obtains from fitting these periods.