Dynamic program analysis can predict data races knowable from an observed execution, but existing predictive analyses either miss races or cannot analyze full program executions. This paper presents Vindicator, a novel, sound (no false races) predictive approach that finds more data races than existing predictive approaches. Vindicator achieves high coverage by using a new, efficient analysis that finds all possible predictable races but may detect false races. Vindicator ensures soundness using a novel algorithm that checks each potential race to determine whether it is a true predictable race. An evaluation using large Java programs shows that Vindicator finds hard-to-detect predictable races that existing sound predictive analyses miss, at a comparable performance cost.