Voronoi diagrams are commonly used to answer traditional nearestneighbor queries in spatial databases. In this work, we propose a new approach to compute Voronoi-cells for the case of uncertain objects having rectangular uncertainty regions. Since exact computation of Voronoi-cells is a hard problem, we instead propose an approximate solution. The main idea of this solution is to apply hierarchical access methods for both data-space and object-space. Our space index is used to efficiently find spatial regions which must (not) be inside a Voronoi-cell. Our object index is used to efficiently identify Delauny-relations, i.e., data objects which affect the shape a Voronoi-cell. We propose and evaluate a number of algorithms to descend both index structures and show that the approach which descends both index structures in parallel yields fast query processing times. Our experiments show that we are able to approximate uncertain Voronoi-cells much more effectively than the state-of-the-art, and at the same time, improve run-time performance.