The low energy limit of string theory contains solutions of large redshift, either near an event horizon or extended objects. Alday, de Boer, and Messamah compared the massless BTZ black hole to the ensemble average of horizonless BPS solutions with the same charges and found them to differ. I will show that averaging gives rise to a spherically symmetric and horizon-free "fivebrane star" solution by employing an effective string description for Type IIA NS5-branes. By further including internal excitations of the extended objects in this description, we obtain solutions of smaller sizes and greater redshifts relative to those with purely transverse excitations, thereby approaching the black hole phase.