This paper presents the zero-truncated negative binomial regression model to estimate the population size in the presence of a single registration file. The model is an alternative to the zero-truncated Poisson regression model and it may be useful if the data are overdispersed due to unobserved heterogeneity. Horvitz–Thompson point and interval estimates for the population size are derived, and the performance of these estimators is evaluated in a simulation study. To illustrate the model, the size of the population of opiate users in the city of Rotterdam is estimated. In comparison to the Poisson model, the zero-truncated negative binomial regression model fits these data better and yields a substantially higher population size estimate.