A compact, two‐stage positron accumulator has been designed, constructed and tested at Swansea, as part of a larger experiment to study Rydberg states of the positronium atom. It uses the well‐understood nitrogen buffer gas technique to trap and accumulate positrons obtained from a Na‐22 radioactive source, and slowed by a solid neon moderator. The main development this system embodies over previous accumulators is reduced physical dimension, made possible by the shorter storage times required. © 2003 American Institute of Physics