In this paper we present a number of techniques that can be at the basis of a practical integration tool for multidimensional databases. We start by addressing the basic issue of matching heterogeneous dimensions and provide a number of general properties that a dimension matching should fulfill. We then propose two different approaches to the problem of integration that try to enforce matchings satisfying these properties. The first approach refers to a scenario of loosely coupled integration, in which we just need to identify the common information between sources and perform drill-across queries over the original sources. The goal of the second approach is the derivation of a materialized view built by merging the sources, and refers to a scenario of tightly coupled integration in which queries are performed against the view. We finally show how these techniques can be actually used to perform drill-across operations over heterogeneous multidimensional information sources.