Provided are a method, system, and article of manufacture for determining whether to use a full volume or repository for a logical copy backup space. A determination is made of a source volume to backup using a logical copy operation. The logical copy operation is completed upon indicating the source volume data to backup. During a logical copy duration, point-in-time data in the source volume as of a point-in-time when the logical copy was established is copied to a backup space in response to receiving an update to the point-in-time data. A history of writes to the source volume is processed to determine whether to allocate a full target volume as the backup space providing a corresponding data unit for each data unit in the source volume or allocate a repository as the backup space, wherein the repository uses less storage space than the full target volume. The logical copy operation using the determined full target volume or repository as the backup space is initiated.