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If one attempts to add momentum-carrying waves to a black string then thesolution develops a singularity at the horizon; this is a manifestation of the'no hair theorem' for black objects. However individual microstates of a blackstring do not have a horizon, and so the above theorem does not apply. Weconstruct a perturbation that adds momentum to a family of microstates of theextremal D1-D5 string. This perturbation is analogous to the 'singleton' modelocalized at the boundary of AdS; to leading order it is pure gauge in the AdSinterior of the geometry.

Momentum-carrying waves on D1-D5 microstate geometries