We report on the principle and realization of a new trap for excitons--the diamond electrostatic trap--which uses a single electrode to create a confining potential for excitons. We also create elevated diamond traps which permit evaporative cooling of the exciton gas. We observe the collection of excitons towards the trap center with increasing exciton density. This effect is due to screening of disorder in the trap by the excitons. As a result, the diamond trap behaves as a smooth parabolic potential which realizes a cold and dense exciton gas at the trap center.