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In this paper we provide a fast, data-driven solution to the failing query problem: given a query that returns an empty answer, how can one relax the query's constraints so that it returns a non-empty set of tuples? We introduce a novel algorithm, loqr, which is designed to relax queries that are in the disjunctive normal form and contain a mixture of discrete and continuous attributes. loqr discovers the implicit relationships that exist among the various domain attributes and then uses this knowledge to relax the constraints from the failing query.In a first step, loqr uses a small, randomly-chosen subset of the target database to learn a set of decision rules that predict whether an attribute's value satisfies the constraints in the failing query; this query-driven operation is performed online for each failing query. In the second step, loqr uses nearest-neighbor techniques to find the learned rule that is the most similar to the failing query; then it uses the attributes' values from this rule to relax the failing query's constraints. Our experiments on six application domains show that loqr is both robust and fast: it successfully relaxes more than 95% of the failing queries, and it takes under a second for processing queries that consist of up to 20 attributes (larger queries of up to 93 attributes are processed in several seconds).