Provided are a computer implemented method, computer program product, and system for creating a consistency group. For each source volume that has an instant virtual copy relationship with a target volume, an indicator for the source volume is set to true in a Fast Incremental with Freeze (FIF) map. The consistency group for each source volume whose indicator is set to true in the FIF map and each associated target volume is created by: performing a quick Instant Virtual Copy (IVC) freeze command to freeze each source volume whose indicator is set to true in the FIF map and performing a consistency group created command to thaw each source volume whose indicator is set to true in the FIF map.