A great number of theoretical papers have been published dealing with the negative positronium ion Ps^–. On the other hand, experimental data on this purely leptonic three-body system (e⁺e^–e^–) is very limited. Apart from a first observation, a lifetime measurement with an accuracy of 4% has been published. We have built a set-up to produce Ps^– making use of moderated positrons from a ²²Na source, and we are presently running an experiment to improve on its decay rate. This paper discusses the status of the project as well as the possibilities of extending these investigations to other properties of Ps^–, the latter becoming possible using the NEPOMUC positron source at the FRM II reactor in Munich.PACS No.: 36.10.Dr