Using the decay of a single exponential function to a nonzero level as an example, the following numerical methods for determining lifetimes are considered: the least-squares method, the differentiation method, and two modifications of the method of moments. Domains of efficient application of one method or the other, depending on the form of the noise distribution, are determined on the basis of computer simulation in parameter space of the problem. For the Poisson noise distribution, a domain of parameters is found, where the error of determining the decay rate in the method of moments is smaller than in the least-squares method.