Provided are a computer program product, system, and method for generating point-in-time copy commands for extents of data. An establish point-in-time copy command is generated for at least one range of extents in at least one volume in the source storage for a point-in-time copy identifier. The at least one range of extents comprises less than all the extents included in the at least one volume. The establish point-in-time copy command is transmitted to a point-in-time copy manager to cause the point-in-time copy manager to create a point-in-time copy for the copy point-in-time identifier and the at least one range of extents, to generate change recording information indicating each of the at least one range of extents, to copy data in the source storage to be updated as changed data, and to indicate in the change recording information the data that has been updated.