We report the laser photoelectron spectra of doubly negatively charged C84 (D2 and D(2d)) using 532 nm and 355 nm radiation. From these spectra, values for the second electron affinity and vertical detachment energy, as well as upper and lower limits for the repulsive Coulomb barrier, are obtained. These values are discussed in the context of classical electrostatic models. The experimental spectra are compared with the accessible excited states of the C-84 product ion calculated in the framework of time dependent density functional theory.