  We perform a detailed study of (supersymmetric) moduli stabilisation in type
IIB toroidal orientifolds with fluxes. We provide strong evidence towards
exhaustion of the finite number of inequivalent vacua for a given total 3-form
flux charge $N_{\rm flux}$. We also find that the minimal value of the string
coupling $g_s$ is given in terms of $N_{\rm flux}$ and present strong evidence
for the asymptotic relation $g_{s,\,\rm{min}}\sim c/N_{\rm flux}^\alpha$, with
$\alpha=1,2$, valid for not too small $N_{\rm flux}$, where $c$ is an order 1
coefficient and $\alpha$ depends on the orbifold. Imposing tadpole
cancellation, $N_{\rm flux}$ is bounded from the number of orientifold
O3-planes. Combined with the flux quantisation, this reduces considerably the
allowed vacua while the lower bound of the string coupling is then not far from
unity. On the other hand, the presence of negative D3-brane charge induced by
magnetised D7-branes breaks supersymmetry and relaxes the bound, allowing
significantly smaller values for $g_s$.
