Mechanisms for backing up at least a portion of storage at a primary computing system to a backup computing system. The primary system identifies primary memory block(s) that have altered content since the time of a last backup. For each such primary block, the primary system estimates whether or not the altered content of the primary block is the same as content of another primary block as the content existed at the time of a specific backup. If they are the same, the primary system backs up the corresponding block by simply informing the backup system of the matching content, and having the backup system write the matching content of other backup block over the respective backup block, rather than transferring the entire block contents.