A method for concurrently converting a standard volume to a thin-provisioned volume includes initially establishing metadata for a thin-provisioned volume. The method then updates the metadata for the thin-provisioned volume to point to extents residing in a standard volume. The method then suspends I/O to metadata for the standard volume. Upon suspending the I/O, the method migrates control of the extents in the standard volume from a standard-volume control algorithm to a thin-provisioned-volume control algorithm. The method then resumes the I/O to the metadata for the thin-provisioned volume. Using this technique, standard volumes may be rapidly converted to thin-provisioned volumes while minimally disrupting I/O to the volumes. A corresponding apparatus and computer program product are also disclosed and claimed herein.