Remote visualization of an arbitrary 2-D planar "cut" from a large volumetric dataset with random access has both gained importance and posed significant challenges over the past few years in industrial and medical applications. In this paper, a prediction model is presented that relates transmission efficiency to voxel coverage statistics for a fast random 2-D image retrieval system. This model can be for parameter selection and also provides insights that lead us to propose a new 3D rectangular tiling scheme, which achieves an additional 10% - 30% reduction in average transmission rate as compared to our previously proposed technique, e.g.,a nearly 30%/45% reduction in the average transmission rate at the cost of a factor of ten/fifteen in storage overhead compared to traditional cubic tiling. Furthermore, this approach leads to improved random access, with less storage and run-time memory required at the client.