In many scattering experiments, the quantity of most direct physical interest is a measure of the difference between two closely related scattering signals, each generated by a Poisson scattering process. This difference is often expressed in terms of an asymmetry statistic, that is, the difference normalized to the sum of the two signals, corrected for an additive background contribution. Typically, a propagation of errors approach is used to compute confidence intervals for asymmetry. However, these confidence intervals are not reliable in general. In this work, generally accurate confidence intervals for asymmetry are obtained using a parametric bootstrap approach. Based on the observed data, data are simulated using a Monte Carlo resampling scheme. The resampled data sets satisfy a constraint that ensures that background‐corrected count rates are not negative.