A method and apparatus for transferring data between two storage media, and is used in an illustrative embodiment to transfer data between two storage media in a shadow set, the storage media being accessible to one or more host processors. The method of the preferred embodiment includes the steps of: A. receiving a command from one of the host processors, the command specifying data to be transferred from a first storage medium to a second storage medium; B. transferring the data specified in the command received from the host from the first storage medium to the second storage medium in a series of subtransfers, each of the subtransfers transferring a portion of the data; and C. processing one or more I/O requests to the shadow set received from one or more host processors by, for each received I/O request: a. implementing the I/O request if the I/O request does not involve a section of the shadow set currently involved in one of the subtransfers; and b. stalling the I/O request if the I/O request involves a section of said shadow set currently involved in one of the subtransfers, and implementing the I/O request when the subtransfer has completed.