1. A method for storing, on a cloud storage site, a secondary copy of an original data set, the method comprising: receiving, with a computing device, a primary copy of an original data set; updating, with the computing device, a content index to reflect at least some of data content in the original data set; identifying, with the computing device, a target cloud storage site on which to store a secondary copy of the original data set, wherein a network connection is to be established between the target cloud storage site and a media file system agent, and wherein the established network connection has an associated latency and bandwidth; determining, with the computing device, a size for a container file to utilize when deduplicating the primary copy of the original data set, wherein the container file size is determined at least in part on the latency, bandwidth, or both, associated with the network connection to be established; deduplicating, with the computing device, at least some of the data content in the primary copy in order to create one or more container files containing deduplicated data, wherein at least one of the container files has the determined size; establishing, with the computing device, the network connection between the target cloud storage site and the media file system agent; and transferring, with the computing device, the one or more container files to the target cloud storage site.