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The problem of deciding containment of aggregate queries is investigated. Containment is reduced to equivalence for queries with expandable aggregation functions. Many common aggregation functions, such as max, cntd (count distinct), count, sum, avg, median and stdev (standard deviation) are shown to be expandable. It is shown that even in the presence of integrity constraints, containment can be reduced to equivalence. For conjunctive count and sum-queries, simpler characterizations for containment are given, that do not require checking equivalence. These results are built upon in order to solve the problem of finding maximally-contained sets of rewritings for conjunctive count-queries.