  We derive the conditions for the one-loop contribution to the cosmological
constant to be exponentially suppressed in a class of heterotic string
compactifications with three generations of chiral matter, where supersymmetry
is spontaneously broken \`a la Scherk-Schwarz. Using techniques of partial
unfolding based on the Hecke congruence subgroup $\Gamma_0(2)$ of the modular
group to extract the leading asymptotics, we show that the super no-scale
condition $n_B=n_F$ between the degeneracies of massless bosons $n_B$ and
fermions $n_F$ in the full string spectrum is necessary but not sufficient, and
needs to be supplemented by additional conditions which we identify. We use
these results to construct three-generation Pati-Salam models with interesting
phenomenological characteristics.
