In this article, a new two-parameter discrete power-Ailamujia (DsPA) distribution is derived using the survival discreti-zation technique. Some key distributional properties and reliability measures are explored in closed forms, such as proba-bility generating function, first four moments and mean residual life. The DsPA parameters are estimated using the max-imum likelihood approach. The performance of this estimation method is assessed via a simulation study. The flexibility of the DsPA distribution is shown using three count datasets. The DsPA distribution provides a better fit than some recent discrete models such as the discrete Burr-XII, uniform Poisson–Ailamujia, Poisson, discrete-Pareto, discrete-Rayleigh, dis-crete inverse-Rayleigh, and discrete Burr–Hutke distributions.