We present experimental results which test whether diffusion engineering can increase the energy resolution of a single-photon superconducting tunnel-junction spectrometer. When a UV photon is absorbed in superconducting Al, it creates an excess number of quasiparticles. If the superconducting absorber is the electrode of a tunnel junction, the quasiparticles tunnel across the voltage-biased junction. The collected charge is proportional to the number of excess quasiparticles. For small energy photons, the initiallycreated charge can be amplified by backtunnelling. The quasiparticles confined around the junction can backtunnel as holes after tunnelling, doubling the output charge, and then tunnel again. The charge multiplication is proportional to the confinement time. When the counterelectrode is terminated with a long, narrow lead, the quasiparticles diffuse out on a time scale set by the dimensions of the leads and of the electrodes, and the diffusion constant of the material. We show how the charge created by the photon varies with the purity of the Al film and with different lead geometries. The experimental results are compared to theoretical predictions of our model. We achieve an energy resolving power of 3 for a photon energy of 3.68 eV. Further investigation of losses in our materials should improve the energy resolution of our diffusion-engineered devices.