Previous research into the efficiency of text retrieval systems has dealt primarily with methods that consider inverted lists in sequence; these methods are known as term-at-a-time methods. However, the literature for optimizing document-at-a-time systems remains sparse.We present an improvement to the max-score optimization, which is the most efficient known document-at-a-time scoring method. Like max-score, our technique, called term bounded max-score, is guaranteed to return exactly the same scores and documents as an unoptimized evaluation, which is particularly useful for query model research. We simulated our technique to explore the problem space, then implemented it in Indri, our large scale language modeling search engine. Tests with the GOV2 corpus on title queries show our method to be 23% faster than max-score alone, and 61% faster than our document-at-a-time baseline. Our optimized query times are competitive with conventional term-at-a-time systems on this year's TREC Terabyte task.