The problem of integrating autonomous data marts arises when, e.g., a large organization (or a federation thereof) needs to combine independently developed data warehouses. It turns out that this problem can be tackled in a systematic way because of two main reasons. First, data marts are usually structured in a rather uniform way, along dimensions and facts. Second, data quality in data marts is usually higher than in generic databases, since they are obtained by reconciling several data sources. Our scenario of reference is a federation of various data marts that we need to query in a unified way by means of drillacross operations. We propose a novel notion of dimension compatibility and characterize its general properties. We then show the significance of dimension compatibility in performing drill-across queries over autonomous data marts.