We consider the problem of computing the complete answer to a
 query when there is limited access to relations, i.e., when binding
 patterns require values to be specified for certain attributes in order
 to retrieve data from a relation.  This problem is common in
 information-integration systems, where heterogeneous sources have diverse
 and limited query capabilities.  A query is {\em stable} if for any
 instance of the relations mentioned in the query, the complete answer to
 the query can be computed, using only the binding patterns permitted for
 queries at the various sources.  We first study conjunctive queries, and
 we show that a conjunctive query is stable if and only if its minimal
 equivalent query $Q_m$ has an order of all the subgoals in $Q_m$, such
 that each subgoal in the order can be queried with a legal binding
 pattern.  We propose two algorithms for testing stability of conjunctive
 queries, and we prove this problem is \N\P-hard.  For a nonstable
 conjunctive query, whether its complete answer can be computed is data
 dependent.  We develop a decision tree that guides the query planning
 process to compute the complete answer to a conjunctive query, if it can
 be computed at all.  We also study stability of unions of conjunctive
 queries, and conjunctive queries with arithmetic comparisons.  In both
 cases we propose algorithms for testing stability of queries.  Finally,
 we study Datalog queries, and prove that if a set of rules and a query
 goal have a feasible rule/goal graph, then the query is stable.