Provided are a method, system, and program for migrating data between storage volumes. A source map is provided indicating blocks of data striped across a first plurality of storage units and a destination map is provided indicating blocks of data striped across a second plurality of storage units, wherein data is migrated from stripes indicated in the source map to corresponding stripes indicated in the destination map. In response to determining that the source stripe and the destination stripe occupy a same physical location on the storage units, the data from a source stripe is written to a copy area and writing the data from the copy area to a corresponding destination stripe.