This paper presents a new approach to estimate an observed space object's shape, while also inferring other attributes, such as its inertial attitude and surface parameters. An adaptive Hamiltonian Markov chain Monte Carlo estimation approach is employed, which uses light-curve data and process inversion to estimate the shape and other attributes. The main advantage of this approach over previous ones is that it can estimate these attributes simultaneously, whereas previous approaches typically rely on a priori knowledge of one or more of them to estimate a particular attribute. Also, unlike previous approaches, the new approach is shown to work well for relatively high dimensions and non-Gaussian distributions of the light-curve-inversion problem. Simulation results involving singleand multiple-faceted objects are shown. Good results are obtained for all cases.