  We count the number of regular supersymmetric solutions in supergravity,
called superstrata, that represent non-linear completion of linear fluctuations
around empty AdS_3 x S^3. These solutions carry the same charges as the D1-D5-P
black hole and represent its microstates. We estimate the entropy using
thermodynamic approximation and find that it is parametrically smaller than the
area-entropy of the D1-D5-P black hole. Therefore, these superstrata based on
AdS_3 x S^3 are not typical microstates of the black hole. What are missing in
the superstrata based on AdS_3 x S^3 are higher and fractional modes in the
dual CFT language. We speculate on what kind of other configurations to look at
as possible realization of those modes in gravity picture, such as superstrata
based on other geometries, as well as other brane configurations.
