whose sensitivity to the value of the cut-off is very weak.

Since the superpotential can be written $W=W_{ISS}+ h W_0$, and $\<W_{ISS}\>=0$ in the global limit, we find that $ m_{3/2} = e^K h
 W_0 + \mathcal{O}(\mu^3) \simeq h W_0$. Hence we only include $m_{3/2}$ in the tables. Also, in all the tables $h$ is taken to be 1. Our main result, concerning the soft mass spectrum, is independent of the precise value of $h$, though we retain full theoretical control in a surprisingly small range. If $h\ll 10^{-1}$ the $\Phi_0$ modulus runs off to the Planck scale as the gravitational effects overwhelm the one-loop contributions (since $\mu$ must go like $\mu
 \rightarrow \frac{\mu}{h}$, as $h$ varies from 1, and hence gravitational effects increase in relevance as $h$ shrinks). However, if $h\gg 1$ the theory becomes strongly coupled.

Our numerical studies show that the non-perturbative piece is under control, that there is only a very mild, logarithmic cut-off dependence, when supergravity corrections are accounted for, and that the main features of the model are independent of $\mu$, assuming $\mu \ll M_P$. These results can be seen in, respectively, tables \[table:Non-pert\], \[table:lam dep\] and \[table:Mu dep\].

From the data in table 