A redundant array of independent data storage libraries of dismountable media units includes parity logging and unique parity update reintegration techniques to improve system performance by reducing the number of media mounts. The media units are arranged into redundancy groups that store the data as sets or parity groups of data blocks and a corresponding parity block. When new data is to be written parity updates are computed and stored in a parity log in nonvolatile storage, such as a magnetic fixed disk drive. The new data blocks are then written onto the media units, but the corresponding new parity blocks are not written if the media units containing the old parity blocks are not mounted at the time the parity updates are computed. If a media unit containing an old parity block is already mounted at the time the parity update is computed, then a new parity block is computed based on the parity update and the new parity block is written to the media unit without logging the parity update. When the media unit containing the old parity block is later mounted on a drive for doing a read or write operation, then the parity update is retrieved from the parity log and the new parity block computed and written to that media unit. The reintegration of parity updates is enhanced by parity pursuit striping wherein successive striping increments of data blocks are mapped across the media units such that a striping increment is located on the same media unit that contains the parity block corresponding to the prior striping increment.