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