This paper addresses the problem of evaluating ranked top-k queries with expensive predicates. As major DBMSs now all support expensive user-defined predicates for Boolean queries, we believe such support for ranked queries will be even more important: First, ranked queries often need to model user-specific concepts of preference, relevance, or similarity, which call for dynamic user-defined functions. Second, middleware systems must incorporate external predicates for integrating autonomous sources typically accessible only by per-object queries. Third, ranked queries often accompany Boolean ranking conditions, which may turn predicates into expensive ones, as the index structure on the predicate built on the base table may be no longer ef...