Quantitative dynamical models of galaxies require deprojection of the observed surface brightness to determine the luminosity density of the galaxy. Existing deprojection methods for axisymmetric galaxies assume that a unique deprojection exists for any given inclination, even though the projected density is known to be degenerate to the addition of ‘konus densities’ that are invisible in projection. We develop a deprojection method based on linear regularization that can explore the range of luminosity densities that are statistically consistent with an observed surface brightness distribution. The luminosity density is poorly constrained at modest inclinations (i ≿ 30°), even in the limit of vanishing observational errors. In constant mass-to-light ratio, axisymmetric, two-integral dynamical models, the uncertainties in the luminosity density result in large uncertainties in the meridional plane velocities. However, the projected line-of-sight velocities show variations comparable to current typical observational uncertainties.