A point in time copy of a data set is provided using a two-phase snapshot copy operation. When a write request is received, as part of the first phase, a chunk including the target location of the write request is determined. Using a "copy on first write" technique, the data at the target location is copied to a snap data area in an allocated data area that is the size of the chunk. A first map for the data set is updated to include up to three entries representing a mapping of the segment including the target location. A second map for the snap data area is updated to include a single entry for the copy of the data from the target location. As part of the second phase, the multiple entries in the first map are coalesced into a single entry after the remaining portions of the chunk are copied to the data area in the snap data area.