Techniques and solutions are described for compressing data and facilitating access to compressed data. Compression can be applied to proper data subsets of a data set, such as to columns of a table. Using various methods, the proper data subsets can be evaluated to be included in a group of proper data subsets to be compressed using a first compression technique, where unselected proper data subsets are not compressed using the first compression technique. Data in the data set can be reordered based on a reordering sequence for the proper data subsets. Reordering data in the data set can improve compression when at least a portion of the proper data subsets are compressed. A data structure is provided that facilitates accessing specified data stored in a compressed format.