In information-integration systems, sources have diverse and
 limited query capabilities.  In a recent paper \cite{Li99-1}, we showed
 that sources not mentioned in a query can contribute to the query result
 by providing useful bindings.  We studied {\em connection queries}, where
 each connection query is a natural join of distinct source views with the
 necessary selection and projection.  Some optimization problems are left
 open, including whether the answer computed by one connection is
 contained in that computed by another connection.  In this paper we study
 this connection-containment problem.  Since \cite{Li99-1} often produces
 a recursive Datalog program to answer a connection query optimally,
 containment seems undecidable.  However, because the Datalog programs of
 \cite{Li99-1} have a special form, their containment can be reduced to
 containment of monadic programs, which is known to be decidable.
 Further, the decidability of monadic Datalog programs involves a complex
 algorithm.  We therefore introduce the question of boundedness for the
 programs of \cite{Li99-1}, and show that boundedness is decidable in
 polynomial time.  We then show in addition that when the contained
 program is bounded, we have a much simpler algorithm for performing the
 containment test.