An asymmetry statistic of physical interest is an estimate of the ratio of the difference and the sum of the Poisson rate parameters for two scattering processes. Typically, an additive background signal contributes to measurements of each signal. Background is measured in a third experiment. Data are corrected by subtracting measured background. When the measured background is larger than one of the other measurements, background‐corrected counts are negative. For this case, it would seem that no useful information can be extracted from the experiment. Here, asymmetry and an associated uncertainty interval are estimated for such cases using a bootstrap approach.