[en] We calculate the electrical and heat currents flowing through a narrow, mesoscopic, normal-metal--superconductor (NS) junction containing a single point impurity. The NS junction exhibits large subgap conduction steps in its current-voltage (I-V) relation when the impurity is located in the normal metal. Our new subgap step appears in the I-V characteristic whenever an additional quasiparticle is trapped between the impurity and NS interface. Locating the impurity inside the superconductor produces both an ''excess current'' and oscillations in the I-V characteristic analogous to the Tomasch effect. A maximum excess current of 2eΔ/h, slightly less than the 8eΔ/3h found for a ballistic NS junction obtains when the impurity is located a few coherence lengths inside the superconductor