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, and having accessor(s) to selectively extract, place and transport cartridges with respect to the cells; operating the accessor(s) to selectively extract, place and transport cartridges with respect to the multi-cartridge deep slot cells and with respect to other elements of the automated data storage library; filling at least the frontmost tier of vacant at least selected multi-cartridge deep slot cells in the selectively extracting, placing and transporting step in accordance with a predetermined algorithm, while leaving other tiers vacant. If the frontmost tier is full, a cartridge is placed into the one of the selected multi-cartridge deep slot cells having the factored greatest number of tiers available to place a cartridge.