Research on logical design of OLAP cubes has tended to assume that the rollup hierarchy in a cube dimension takes the form of a balanced tree. However, experience from industry indicates that a much broader class of rollup hierarchies is of interest in practice. For example, the hierarchy tree might be unbalanced or ragged (or both), or indeed the hierarchy might not be a tree at all, but a more general acyclic directed graph structure such as a lattice. We demonstrate how dependency information can assist in the design of aggregation hierarchies. In addition to dependencies familiar from relational database theory, we use new classes of dependencies to extend logical design principles so that they include this more general notion of cube dimension hierarchies.