De-duplication operations are applied to mirror volumes. Data stored to a first volume is mirrored to a second volume. The second volume is a virtual volume having a plurality of logical addresses, such that segments of physical storage capacity are allocated for a specified logical address as needed when data is stored to the specified logical address. A de-duplication operation is carried out on the second volume following a split from the first volume. A particular segment of the second volume is identified as having data that is the same as another segment in the second volume or in the same consistency group. A link is created from the particular segment to the other segment and the particular segment is released from the second volume so that physical storage capacity required for the second volume is reduced.