Search engines need to evaluate queries extremely fast, a challenging task given the quantities of data being indexed. A significant proportion of the queries posed to search engines involve phrases. In this article we consider how phrase queries can be efficiently supported with low disk overheads. Our previous research has shown that phrase queries can be rapidly evaluated using nextword indexes, but these indexes are twice as large as conventional inverted files. Alternatively, special-purpose phrase indexes can be used, but it is not feasible to index all phrases. We propose combinations of nextword indexes and phrase indexes with inverted files as a solution to this problem. Our experiments show that combined use of a partial nextword, partial phrase, and conventional inverted index allows evaluation of phrase queries in a quarter the time required to evaluate such queries with an inverted file alone; the additional space overhead is only 26% of the size of the inverted file.