A search query consists of several words. In a proximity fulltext search, we want to find documents that contain these words near each other. This task requires much time when the query consists of highfrequently occurring words. If we cannot avoid this task by excluding high-frequently occurring words from consideration by declaring them as stop words, then we can optimize our solution by introducing additional indexes for faster execution. In a previous work, we discussed how to decrease the search time with multi-component key indexes. We had shown that additional indexes can be used to improve the average query execution time up to 130 times if queries consisted of high-frequently occurring words. In this paper, we present another search algorithm that overcomes some limitations of our previous algorithm and provides even more performance gain.