A method of operating a data processing system having a main memory divided into memory pages that are swapped into and out of main memory when the main memory becomes short. The data processing system has an operating system that sends page store commands specifying memory pages to be stored in a swap file and page retrieve commands specifying memory pages to be retrieved from the swap file and stored in the main memory. The present invention provides a swap driver that utilizes compression code for converting one of the memory pages that is to be swapped out of main memory to a compressed memory page. The data processing memory includes a compressed page region that is used to store the compressed memory pages. A page table in the compressed page region specifies the location of each compressed page and the page address corresponding to that page. The swap driver compresses at least one of the memory pages specified in one of the page store commands to provide a corresponding compressed memory page and causes that compressed memory page to be stored in the compressed page region. The swap driver also searches the page table for a page identified in one of the retrieve commands. The swap driver causes that page to be moved to a corresponding area of main memory after decompressing the page if the swap driver finds an entry in the page table indicating that the page is stored in the compressed page region.