The Skellam model describes discrete-time population dynamics of a single species assuming uniform (i.e., random or Poissonian) individual distribution and intraspecific contest competition. Apart from studies on individual-based models derived from first principles, it has rarely been applied to ecological research. However, in specific situations, it may be more appropriate than, for instance, the frequently used Ricker model. This is derived from assuming scramble competition among individuals. In this paper, we offer insight into the first principles underlying the Skellam model. In addition, we provide an alternative parameterization of the model in terms of two commonly used parameters: intrinsic rate of population increase and carrying capacity. In light of these findings, the Skellam model may be a useful alternative for a range of purposes where it has previously been overlooked, e.g., in fitting population models to time series data.