In this paper a rate-equation model is developed for a single-wavelength dye laser. The model is unique in that it accounts for the fact that triplet-state lifetimes are not necessarily very long, as has been previously assumed. This modification makes it possible to analyze more accurately the behavior of dye lasers that are pumped with pulse energies above threshold. Computer solutions of the rate equations are obtained and an experimental technique is developed to measure amplifier gain, which is then used to estimate populations of molecules at various energy levels. An experimental study of triplet lifetimes in anthracene is included in an Appendix. These results support the experimental values obtained by Stockman for Rhodamine 6G, which are used in our calculations.