We present predictions for a diffusion-engineered, single-photon spectrometer in the UV-visible range using a superconducting tunnel junction. Quasiparticles are created by photoexcitation, with charge Q 0 . After tunneling through the junction, the quasiparticles can either backtunnel or diffuse away. With confinement by a higher gap or by narrow leads the quasiparticles in the counterelectrode dwell next to the junction and backtunnel, increasing the collected charge to Q ¼ pQ 0 ; p>1. For very narrow leads the dwell time is inversely proportional to the lead width, up to the recombination time of Al, 1 ms at 0.2 K. The new aspect of our work is the use of narrow leads to control the charge gain p, while minimizing self-heating. This charge gain will improve the energy resolution compared to the case p ¼ 1; where the electronic noise is dominant, and compared to much larger charge gain, pE50, where large self-heating resulted with extra noise. r