A storage controller receives a request to establish a point-in-time copy operation by placing a space efficient source volume in a point-in-time copy relationship with a space efficient target volume, wherein subsequent to being established the point-in-time copy operation is configurable to consistently copy the space efficient source volume to the space efficient target volume at a point in time. A determination is made as to whether any track of an extent is staging into a cache from the space efficient target volume or destaging from the cache to the space efficient target volume. In response to a determination that at least one track of the extent is staging into the cache from the space efficient target volume or destaging from the cache to the space efficient target volume, release of the extent from the space efficient target volume is avoided.