1. A computer program product comprising at least one non-transitory computer-readable storage medium storing computer-executable code for a travel reservation search engine to execute search requests, the computer-executable code comprising: a query interface module configured to receive from a user a search request for travel reservation information, the search request including at least one first constraint to be met by results returned by a search; a constraint evaluation module configured to: select at least one additional constraint not included in the search request; construct a first query based on the at least one first constraint and the at least one additional constraint such that fewer search results are obtained in response to executing the first query than would be obtained in response to executing a query constructed without the at least one additional constraint; and construct a second query based on the at least one first search constraint without the at least one additional constraint; wherein the select at least one additional constraint is performed based on an estimated execution time of the first query with the at least one additional constraint; and a website query module configured to execute the first query to obtain first phase query results and the second query to obtain second phase query results, wherein the first phase query results and the second phase query results are non-intersecting.