1. A data storage system that encrypts secondary copies of data, the system comprising: at least one computer processor comprising computer hardware, the computer processor configured to perform a storage operation that creates at least one secondary copy of data; the computer processor further configured to calculate a completion time to create and encrypt at least a portion of the secondary copy; when the completion time exceeds a threshold time, the computer processor is configured to transfer the secondary copy to at least one storage device without encrypting at least a portion of the secondary copy, and after transfer, encrypt one or more unencrypted portions of the secondary copy; and when the completion time is less than the threshold time, the computer processor is configured to encrypt at least a portion of the secondary copy in association with performing the storage operation.