A user can set or modify operational parameters of a data volume stored on a network-accessible storage device in a data center. For example, the user may be provided access to a data volume and may request a modification to the operational parameters of the data volume. Instead of modifying the existing data volume, the data center can provision a new data volume and migrate data stored on the existing data volume to the new data volume. While the data migration takes place, the existing data volume may block input/output (I/O) requests and the new data volume may handle such requests instead. If a request is received for data not yet migrated to the new data volume, then the new data volume prioritizes a migration of the requested data.