  A class of axially symmetric, rotating four-dimensional geometries carrying
D1, D5, KK monopole and momentum charges is constructed. The geometries are
found to be free of horizons and singulaties, and are candidates to be the
gravity duals of microstates of the (0,4) CFT. These geometries are constructed
by performing singularity analysis on a suitably chosen class of solutions of
six-dimensional minimal supergravity written over a Gibbons-Hawking base
metric. The properties of the solutions raise some interesting questions
regarding the CFT.
