Our work is motivated by the problem of managing data on storage devices, typically a set of disks. Such storage servers are used as web servers or multimedia servers, for handling high demand for data. As the system is running, it needs to dynamically respond to changes in demand for different data items. There are known algorithms for mapping demand to a layout. When the demand changes, a new layout is computed. In this work we study the data migration problem, which arises when we need to quickly change one layout to another. This problem has been studied earlier when for each disk the new layout has been prescribed. However, to apply these algorithms effectively, we identify another problem that we refer to as the correspondence problem, whose solution has a significant impact on the solution for the data migration problem. We study algorithms for the data migration problem in more detail and identify variations of the basic algorithm that seem to improve performance in practice, even though some of the variations have poor worst case behavior.