A directory and members are allocated to store a data set, wherein the directory stores pointers to the members to allow data stored in the members to be accessed. The directory is expanded to accommodate an expansion of the data set, causing the directory to be stored in non-contiguous pages and becoming fragmented. A computational device determines that a threshold that measures a level of fragmentation of the directory relative to an amount of storage allocated for the data set has been exceeded. The computational device reorganizes the fragmented directory, into a reorganized directory that is stored in contiguous pages at the end of the data set, in response to determining that the threshold has been exceeded.