The precomputation of the different summary views of a data cube is critical to improving the response time of data cube queries for On-Line Analytical Processing (OLAP). The computation of the full data cube, representing all 2d views, has been studied extensively. However, the full cube is often too large to be computed and stored, and for some applications all views are not even required. Hence, it is important to provide efficient methods for the computation of partial data cubes consisting of an arbitrary, user selected, subset of the 2d possible views. In this paper, we study the top-down computation of partial ROLAP data cubes. We present both sequential and parallel methods for top-down partial data cube construction. Our experimental results indicate close to linear performance improvement for partial data cube computation. For example, when selecting 50% of the views our method requires only 55% of the time required to build the full cube, and when selecting 75% of the views our method requires just 82% of the full cube time.