Large search engines process thousands of queries per second over billions of documents, making query processing a major performance bottleneck. An important class of optimization techniques called early termination achieves faster query processing by avoiding the scoring of documents that are unlikely to be in the top results. We study new algorithms for early termination that outperform previous methods. In particular, we focus on safe techniques for disjunctive queries, which return the same result as an exhaustive evaluation over the disjunction of the query terms. The current state-of-the-art methods for this case, the WAND algorithm by Broder et al.  and the approach of Strohman and Croft , achieve great benefits but still leave a large performance gap between disjunctive and (even non-early terminated) conjunctive queries. We propose a new set of algorithms by introducing a simple augmented inverted index structure called a block-max index. Essentially, this is a structure that stores the maximum impact score for each block of a compressed inverted list in uncompressed form, thus enabling us to skip large parts of the lists. We show how to integrate this structure into the WAND approach, leading to considerable performance gains. We then describe extensions to a layered index organization, and to indexes with reassigned document IDs, that achieve additional gains that narrow the gap between disjunctive and conjunctive top-k query processing.