An innovative technique supporting accuracy control in compressed multidimensional data cubes is presented in this paper. The proposed technique can be efficiently used in QoA-based OLAP tools, where OLAP users/applications and DW servers are allowed to mediate on the accuracy of (approximate) answers, similarly to what happens in QoS-based systems for the quality of services. The compressed data structure KLSA, which implements the technique, is also extensively presented and discussed. We complement our analytical contributions with an experimental evaluation on several kinds of synthetic multidimensional data cubes, demonstrating the superiority of our approach in comparison with other similar techniques.