Searching XML data with a structured XML query can improve the precision of results compared with a keyword search. However, the structural heterogeneity of the large number of XML data sources makes it difficult to answer the structured query exactly. As such, query relaxation is necessary. Previous work on XML query relaxation poses the problem of unnecessary computation of a big number of unqualified relaxed queries. To address this issue, we propose an adaptive relaxation approach which relaxes a query against different data sources differently based on their conformed schemas. In this paper, we present a set of techniques that supports this approach, which includes schema-aware relaxation rules for relaxing a query adaptively, a weighted model for ranking relaxed queries, and algorithms for adaptive relaxation of a query and top-k query processing. We discuss results from a comprehensive set of experiments that show the effectiveness and the efficiency of our approach. © 2010 Elsevier B.V. All rights reserved.