Resampling is the process of selecting from a set of candidate samples to achieve a distribution (approximately) proportional to a desired target. Recent work has revisited its application to Monte Carlo integration, yielding powerful and practical importance resampling methods. One drawback of these methods is that they cannot generate stratified samples. We propose a method to achieve efficient stratification. We first introduce a discrete sampling algorithm which yields the same result as conventional inverse CDF sampling but in a single pass over the candidates, without needing to store them, similarly to reservoir sampling. We order the candidates along a space-filling curve to ensure that stratified CDF sampling of candidate indices yields stratified samples in the integration domain. We showcase our method on various resampling-based rendering problems.