  The geometries describing D1-D5-P bound states in string theory have three
regions: flat asymptotics, an anti-de Sitter throat, and a 'cap' region at the
bottom of the throat. We identify the CFT description of a known class of
supersymmetric D1-D5-P microstate geometries which describe degrees of freedom
in the cap region. The class includes both regular solutions and solutions with
conical defects, and generalizes configurations with known CFT descriptions: a
parameter related to spectral flow in the CFT is generalized from integer to
fractional values. We provide strong evidence for this identification by
comparing the massless scalar excitation spectrum between gravity and CFT and
finding exact agreement.
