Neyman-Pearson confidence intervals for extreme low-level, paired counting

Neyman-Pearson principles are briefly discussed and 95% confidence intervals of the form [0, ##.##] are presented. Use is made of the fact that the probability of the difference of two random variables, each with a Poisson distribution, can be expressed in terms of modified Bessel functions of integral order and elementary functions. The validity of the values is discussed.