We propose a new hierarchical approach to resolution scalable lossless and near-lossless (NLS) compression. It combines the adaptability of DPCM schemes with new hierarchical oriented predictors to provide resolution scalability with better compression performances than the usual hierarchical interpolation predictor or the wavelet transform. Because the proposed hierarchical oriented prediction (HOP) is not really efficient on smooth images, we also introduce new predictors, which are dynamically optimized using a least-square criterion. Lossless compression results, which are obtained on a large-scale medical image database, are more than 4% better on CTs and 9% better on MRIs than resolution scalable JPEG-2000 (J2K) and close to nonscalable CALIC. The HOP algorithm is also well suited for NLS compression, providing an interesting rate-distortion tradeoff compared with JPEG-LS and equivalent or a better PSNR than J2K for a high bit rate on noisy (native) medical images.