  From the analysis of the near horizon geometry and supersymmetry algebra it
has been argued that all the microstates of single centered BPS black holes
with four unbroken supersymmetries carry zero angular momentum in the region of
the moduli space where the black hole description is valid. A stronger form of
the conjecture would be that the result holds for any sufficiently generic
point in the moduli space. In this paper we set out to test this conjecture for
a class of black hole microstates in type II string theory on $T^6$,
represented by four stacks of D-branes wrapped on various cycles of $T^6$. For
this system the above conjecture translates to the statement that the moduli
space of classical vacua must be a collection of points. Explicit analysis of
systems carrying a low number of D-branes supports this conjecture.
