We consider the problem of selecting the auxiliary distribution to implement the wild bootstrap for regressions featuring heteroscedasticity of unknown form. Asymptotic refinements are nominally obtained by choosing a distribution with second and third moments equal to 1. We show that this stipulation may fail in practice, due to the distortion imposed on higher moments. We propose a new class of two-point distributions and suggest using the Kolmogorov-Smirnov statistic as a selection criterion. The results are illustrated by a Monte Carlo experiment.