Provided are a computer program product, system, and method for managing point-in-time copies for extents of data. A point-in-time copy for at least one range of extents in at least one volume for a point-in-time copy identifier is established. Change recording information is generated indicating each of the at least one range of extents less than all of the extents in the at least one volume. An update to data in the at least one range of extents in the point-in-time copy is received and data in the source storage in the at least one range of extents to be updated is copied as changed data to the target storage. Indication is made in the change recording information of the data in the at least one range of extents that has been updated.