In one embodiment, a local copy target is also a local primary of an incomplete consistency group of an ongoing asynchronous mirror relationship. Completion of the consistency group is facilitated notwithstanding that the local copy operation was initiated after the consistency group was initiated. In one aspect, asynchronous data mirroring logic, prior to the overwriting of existing data of the target, reads the existing data of the target for purposes of mirroring the read data to a remote secondary target of the consistency group. As a result, existing data of the local copy target which is also a local primary source of the consistency group, may be safely overwritten. Other features and aspects may be realized, depending upon the particular application.