A computer-implemented method, according to one embodiment, includes: estimating, by the computer system, a waiting time for copy target data to be transferred from the source medium. The waiting time includes an estimated time for locating and reading the copy target data from the source medium. The method also includes selecting, by the computer system, migration target data on the source medium based on whether migration of data to the target medium is expected to be finished within the waiting time. The selecting is based at least in part on comparing a size of the data and an allowable size calculated based on the waiting time and an estimated write transfer rate to the target medium. The method further includes migrating, by the computer system, the migration target data from the source medium to the target medium.