Shear-banding is the phenomenon where macroscop-ically large regions (the "bands"), with differing mi-crostructural properties, coexist under the influence of shear flow. Banded structures are found at very low shear-rates, far below the shear-rate where the Taylor in-stability occurs. The final stationary state often depends on whether the flow is applied under controlled stress or shear-rate conditions [1, 2]. In a cylindrical geometry, bands are either alternately stacked in the vorticity direc-tion or layered around the inner cylinder in the gradient direction. A well studied system that exhibits this com-plex behavior are dispersions of wormlike micelles under shear. Depending on the concentration of monomers and flow conditions, a variety of phase transitions and struc-tural changes are observed [1, 3]. These experiments are theoretically described by Cates [4]. Wormlike micelles have a significant chain flexibility and they permanently exchange material (i.e. they can break and recombine). This complicates the physics of shear-banding consider-ably.