In this work, near-lossless compression, i.e., yielding strictly bounded reconstruction error, is proposed for high-quality compression of remote sensing images. First, a classified causal DP CM scheme is presented for optical data, either multi/hyperspectral (3D), or panchromatic (2D) observations. It is based on a classified linear-regression prediction, followed by context-based arithmetic coding of the outcome prediction errors, and provides excellent performances, both for reversible and for irreversible, i.e., near-lossless, compression. Coding time are affordable thanks to fast convergence of training. Decoding is always performed in real time. Then, an original approach to near-lossless compression of SAR images that is based on the Rational Laplacian Pyramid (RLP) is presented. The baseband icon of the RLP is DPCM encoded, the intermediate layers are uniformly quantized, and the bottom layer is is logarithmically quantized. As a consequence, the relative error, i.e., pixel ratio of original to decoded image, can be strictly bounded by the quantization step size of the bottom layer of RLP. The step sizes on the other layers are chosen as minimizing the bit rate for a given distortion, by exploiting the quantization noise feedback loops at the encoder. In both cases, if the reconstruction errors fall within the boundaries of the noise distributions, either digitization noise, or speckle, the decoded images will be virtually lossless, even though their encoding is not strictly reversible.