Mass and radius of planets transiting their host stars are provided by radial velocity and photometric observations. Structural models of solid exoplanet interiors are then constructed by using equations of state for the radial density distribution, which are compliant with the thermodynamics of the high-pressure limit. However, to some extent those structural models suffer from inherent degeneracy or non-uniqueness problems owing to a principal lack of knowledge of the internal differentiation state and/or the possible presence of an optically thick atmosphere. We here discuss the role of corresponding measurement errors, which adversely affect determinations of a planet's mean density and bulk chemical composition. Precise measurements of planet radii will become increasingly important as key observational constraints for radial density models of individual solid low-mass exoplanets or super-Earths.