1. A computer-implemented method, comprising: under control of a storage-management server, storing metadata about data objects in a database; in response to a request to delete one or more data objects stored in data storage, logically deleting the one or more data objects by deleting the metadata about the one or more data objects in the database; and sending a notification that the one or more data objects have been logically deleted by deleting the metadata about the one or more data objects, wherein the notification provides storage locations within one or more logical storage volumes corresponding to the deleted one or more data objects, wherein each of the one or more data objects are divided into one or more extents; and under control of a deduplicating storage system that is separate from and coupled to the storage-management server, receiving the notification; and in response to determining that a sparse file represents the one or more logical storage volumes, recovering the physical space occupied by unused extents without moving data and without forcing updates to storage location information tracked by the storage-management server by nulling out space in the sparse file corresponding to each of the one or more extents.