The response of a position-sensitive Li-glass based scintillation detector being developed for thermal-neutron detection with 6 mm position resolution has been investigated using focused beams of 2.5MeV protons and deuterons. The beams were scanned across the detector in 0.5 mm horizontal and vertical steps perpendicular to the beams. Scintillation light was registered using an 8 × 8 pixel multi-anode photomultiplier tube. The signal amplitudes were recorded for each pixel on an event-by-event basis. Several pixels generally registered considerable signals at each beam location. To optimize planned detector operation at the European Spallation Source, the number of pixels above set thresholds was investigated, with the maximization of the single-hit efficiency over the largest possible area as the primary goal. For both beams, at a threshold of ∼50% of the mean of the full-deposition peak, ∼80% of the events were registered in a single pixel, resulting in an effective position resolution of ∼5 mm in X and Y. Lower thresholds resulted in higher pixel multiplicities. These events could also be localized with the same effective position resolution.