Data Warehousing requires effective methods for processing and storing large amounts of data. OLAP applications form an additional tier in the data warehouse architecture and in order to interact acceptably with the user, typically data pre-computation is required. In such a case compressed representations have the potential to improve storage and processing efficiency. This paper proposes a compressed database system which aims to provide an effective storage model. We show that in several other stages of the Data Warehouse architecture compression can also be employed. Novel systems engineering is adopted to ensure that compression/decompression overheads are limited, and that data reorganisations are of controlled complexity and can be carried out incrementally. The basic architecture is described and experimental results on the TPC-D and other datasets show the performance of our system.