The production of single photons using rephased amplified spontaneous emission is examined. This process produces single photons on demand with high efficiency by detecting the spontaneous emission from an atomic ensemble, then applying a population-inverting pulse to rephase the ensemble and produce a photon echo of the spontaneous emission events. The theoretical limits on the efficiency of the production are determined for several variants of the scheme. For an ensemble of uniform optical density, generating the initial spontaneous emission and its echo using transitions of different strengths is shown to produce single photons at 70% efficiency, limited by reabsorption. Tailoring the spatial and spectral density of the atomic ensemble is then shown to prevent reabsorption of the rephased photon, resulting in emission efficiency near unity.