  We consider compactifications of type II string theory using exact internal
CFT's with central charge $c=9+\epsilon$, $|\epsilon| \ll 1$, leading to an
effective potential for the dilaton. For $\epsilon>0$ the potential is positive
and the dilaton is ultimately driven to weak coupling. For $\epsilon<0$ the
dilaton is driven to strong coupling, but we can stabilise the background by
including D-branes. The resulting minimum admits an $AdS_4$ solution where the
cosmological constant is of the order $\epsilon^3$ and the string coupling
constant is of order $\epsilon$. Furthermore these CFT's typically do not
possess any massless or tachyonic modes. Thus these vacua provide exact CFT
descriptions of moduli stabilisation in weakly coupled string theory.
