  We discuss "spectral flow" coordinate transformations that take
asymptotically four-dimensional solutions into other asymptotically
four-dimensional solutions. We find that spectral flow can relate smooth
three-charge solutions with a multi-center Taub-NUT base to solutions where one
or several Taub-NUT centers are replaced by two-charge supertubes, and vice
versa. We further show that multi-parameter spectral flows can map such
Taub-NUT centers to more singular centers that are either D2-D0 or pure
D0-brane sources. Since supertubes can depend on arbitrary functions, we
establish that the moduli space of smooth horizonless black hole microstate
solutions is classically of infinite dimension. We also use the physics of
supertubes to argue that some multi-center solutions that appear to be bound
states from a four-dimensional perspective are in fact not bound states when
considered from a five- or six-dimensional perspective.
