In this paper, a novel multiple description coding technique is proposed, based on optimal Lagrangian rate allocation. The method assumes the coded data consists of independently coded blocks. Initially, all the blocks are coded at two different rates. Then blocks are split into two subsets with similar rate distortion characteristics; two balanced descriptions are generated by combining code blocks belonging to the two subsets encoded at opposite rates. A theoretical analysis of the approach is carried out, and the optimal rate distortion conditions are worked out. The method is successfully applied to the JPEG 2000 standard and simulation results show a noticeable performance improvement with respect to state-of-the art algorithms. The proposed technique enables easy tuning of the required coding redundancy. Moreover, the generated streams are fully compatible with Part 1 of the standard.