Two-dimensional compressed data sets can be re-aligned while preserving compression of the data. A set of one or more shifts and a corresponding set of one or more first dimension indices into a two-dimensional compressed data set for re-aligning the two-dimensional compressed data set are determined. Impact of re-aligning upon each vector in the second dimension of the two-dimensional compressed data set is determined while the two-dimensional compressed data set remains compressed. New compressed vectors are created in the second dimension resulting from re-aligning. Compression information is modified for each of the original vectors of the two-dimensional compressed data set that remain after re-aligning based, at least in part, on the new compressed vectors. A re-aligned version of the two-dimensional compressed data set is created with the new compressed vectors, and the remaining original vectors with their modified compression information.