In an automated data storage library having a plurality of multi-cartridge deep slot cells, each configured to store a plurality of data storage cartridges arranged in sequential order of tiers from front to rear; having a plurality of single cartridge storage slots; and having accessor(s) configured to selectively extract, place and transport cartridges with respect to the cells; operating the accessor(s) to selectively extract, place and transport data storage cartridges with respect to the multi-cartridge deep slot cells and the storage slots, and with respect to other elements of the automated data storage library; and, if a data storage cartridge is recently used by and is to be demounted from a selected other element of the automated data storage library: first, extracting another data storage cartridge from the storage slots, vacating one of the storage slots; and second, extracting, transporting and placing the demounted data storage cartridge in the vacated storage slot.