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