© 2017 Informa UK Limited, trading as Taylor & Francis Group. This article extends a rate-allocation method based on the near-lossless-rate (NLR) complexity that is designed to operate on-board spacecrafts, to include support for distortion scaling factors, such as those that are needed to code multi- and hyperspectral image when a spectral transform is employed. In this article, the conditions to achieve global minimum distortion are derived under the rate-distortion model based on the NLR complexity for the case of varying distortion scaling factors. Practical implementation issues are dealt with, and a rate-allocation method capable of operating under the constraints of on-board operation is provided. An exhaustive experimental validation of the rate-allocation method is performed, reporting modest performances for low rates and close to optimal performances for high rates.