Provided are a computer program product, system, and method for an application to provide for, in one embodiment, using hierarchical storage management to respond to a request to delete a data set by migrating the data set to another storage tier in a storage system before deleting the data set from its current location. As a result, the data set is stored on another tier to provide an opportunity to reverse the decision to delete the data set. In one embodiment, a temporary interval of time is provided to reverse the deletion decision and restore the data set from the migrated data set, before the data set is permanently deleted.