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A useful tool to construct wavelet decompositions is the lifting scheme. The generalized lifting is an extension of the classical lifting scheme to introduce more flexibility and to permit the creation of new nonlinear and adaptive transforms. However, the design of generalized prediction and update steps is more involved. This letter proposes a generalized prediction design that minimizes the detail signal energy and entropy at the same time. Two algorithm variants are given. The fixed prediction uses the image class statistics to derive the optimal transform. If the statistics are unknown, the adaptive prediction extracts them from the image being coded. The resulting decompositions are applied to lossless image coding, reporting good results. The adaptive algorithm has no bookkeeping or side information requirements, yet its performance is close to the fixed prediction performance.