  We consider the space of boundary conditions of Virasoro minimal models
formed from the composition of a collection of flows generated by \phi_{1,3}.
These have recently been shown to fall naturally into a sequence, each term
having a coordinate on it in terms of a boundary parameter, but no global
parameter has been proposed. Here we investigate the idea that the overlaps of
particular bulk states with the boundary states give natural coordinates on the
moduli space of boundary conditions. We find formulae for these overlaps using
the known thermodynamic Bethe Ansatz descriptions of the ground and first
excited state on the cylinder and show that they give a global coordinate on
the space of boundary conditions, showing it is smooth and compact as expected.
