This proposal aims to avoid the “Statistical Paradox” showed by Lindley (1957) and the misuse of canonical values of significance. Adaptive significance levels are applied to compare the means of two Poisson distributions with unknown parameters. For this propose, the analysis is carried out by conditioning on a suitable statistic in order to make use of Berger and Wolpert’s principle of the non-informative nuisance parameter J. and R. (1988).