The present invention is a system and method which allows for a VTL system that supports thin provisioning to implicitly unmap unused storage. Such unmap operations may occur even though the VTL system does not receive any explicit unmap requests from its initiators. For example, if a system administrator knows that once a virtual tape drive of the VTL system has been partially overwritten, all previously written data sets on that virtual tape drive will never again be accessed, the system administrator may configure the VTL system so that it unmaps the entire remainder of the virtual tape drive on the first data overwrite.