A structured query may specify attribute values for attributes. An estimate of the number of items that will match the structured query if it is applied to a structured database is determined. If the estimated number of items is below a threshold, the structured query may be relaxed to form new candidate structured queries. The number of candidate queries may be determined based on a desired running time. Each of the candidate structured queries may be determined by changing one or more attribute values of the attributes of the structured query. Estimates of the number of items each of the candidate structured queries will match is determined, and the candidate structured query that has the highest matching estimation is used to query the database. The matching results may be output.