Central to the study of dust-plasma interactions in the solar system is the electrostatic charging of dust grains. While previous calculations have generally assumed that the distributions of electrons and ions in the plasma are Maxwellian, most space plasmas are observed to have non-Maxwellian tails and can often be fit by a generalized Lorentzian (kappa) distribution. Here we use such a distribution to reevaluate the grain potential, under the condition that the dominant currents to the grain are due to electron and ion collection, as is the case in certain regions of space. The magnitude of the grain potential is found to be larger than that in a Maxwellian plasma as long as the electrons are described by a kappa distribution: this enhancement increases with ion mass and decreasing electron kappa. The modification of the grain potential in generalized Lorentzian plasmas has implications for both the physics (e.g., grain growth and disruption) and the dynamics of dust in space plasmas. These are also briefly discussed in this short note. ¿ American Geophysical Union 1992