In this study, calculation of decision threshold and detection limit expressed in counts for low-level radioactivity measurements were evaluated and compared to a Monte Carlo method for the case of paired Poisson-distributed observations, i.e. for discrete variables. The calculated characteristic limits obtained from Monte Carlo calculations were compared with analytical expressions given in literature. The results in this study show that the equations given by Currie are in good agreement with the results from the Monte Carlo calculations simulating nuclear counting applications with a low number of observed counts. An exception is observed for a background corresponding to zero counts. This study also shows that at a low number of counts, the specific boundary conditions of the interval that represents counts corresponding to the presence of the analyte (>or ≥), have an impact on the false positives and negatives rates as defined by the parameters α and β.