Data marts storing pre-aggregated data, prepared for further roll-ups, play an essential role in data warehouse environments and lead to significant performance gains in the query evaluation. However, in order to ensure the completeness of query results on the data mart without to access the underlying data warehouse, null values need to be stored explicitly; this process is denoted as negative caching. Such null values typically occur in multidimensional data sets, which are naturally very sparse. To our knowledge, there is no work on shrinking the null tuples in a multi-dimensional data set within ROLAP. For these tuples, we propose a lossless compression technique, leading to a dramatic reduction in size of the data mart. Queries depending on null value information can be answered with 100% precision by partially inflating the shrunken data mart. We complement our analytical approach with an experimental evaluation using real and synthetic data sets, and demonstrate our results.