A technique for processing a request requiring that a first volume of removable storage media be mounted on a storage device is disclosed. It is determined whether the storage device is available. In the event it is determined that the storage device is not available because it currently has mounted on it a second volume of removable storage media associated with a data mover, it is determined whether the data mover should be asked to permit the second volume to be removed from the storage device so that the first volume can be mounted thereon. In the event it is determined that the data mover should be asked to permit the second volume to be removed from the storage device so that the first volume can be mounted thereon, the data mover is prompted to provide an indication that the second volume may be dismounted from the storage device.