Innovations in performing sort operations for dictionary-compressed values of columns in a column-store database using value identifiers (“IDs”) are described. For example, a database system includes a data store and an execution engine. The data store stores values at positions of a column A dictionary maps distinct values to corresponding value IDs. An inverted index stores, for each of the corresponding value IDs, a list of those of the positions that contain the associated distinct value. The execution engine processes a request to sort values at an input set of the positions and identify an output set of the positions for sorted values. In particular, the execution engine iterates through positions stored in the lists of the inverted index. For a given position, the execution engine checks if the given position is one of the input set and, if so, adds the given position to the output set.