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In information-integration systems, sources may have diverse and limited query capabilities. To obtain maximum information from these restrictive sources to answer a query, one can access sources that are not specified in the query (i.e., off-query sources). In this article, we propose a query-planning framework to answer queries in the presence of limited access patterns. In the framework, a query and source descriptions are translated to a recursive datalog program. We then solve optimization problems in this framework, including how to decide whether accessing off-query sources is necessary, how to choose useful sources for a query, and how to test query containment. We develop algorithms to solve these problems, and thus construct an efficient program to answer a query.