The On-Line Analytical Processing is an emerging technique for the implementation of decision support applications that access remote datacubes over information highways. In this paper, we propose a novel approach for sending datacubes over congested networks, so that, in order to preserve fast response time, some datacube tuple can be eventually lost but preserving a good approximation of the overall datacube. The main idea is to prioritize the datacube information and to send it using a priority-based transmission protocol.The proposed method relies on two well-known techniques: the wavelet decomposition, for the encoding of the datacube into a sequence of prioritized coefficients, and the Priority Encoding Transmission protocol, to delivery them. To reconstruct the datacube with a user-defined error level, priorities are assigned using a thresholding technique. Preliminary experimental results are very encouraging.