  We analyse a new ${\cal N}=1$ string tree level correction at ${\cal
O}(\alpha'^2)$ to the K\"ahler potential of the volume moduli of type IIB
Calabi-Yau flux compactification found recently by Grimm, Savelli and
Weissenbacher~\cite{Grimm:2013gma} and its impact on the moduli potential. We
find that it imposes a strong lower bound the Calabi-Yau volume in the Large
Volume Scenario of moduli stabilisation. For KKLT-like scenarios we find that
consistency of the action imposes an upper bound on the flux superpotential
$|W_0|\lesssim 10^{-3}$, while parametrically controlled survival of the KKLT
minimum needs extreme tuning of $W_0$ close to zero. We also analyse the
K\"ahler uplifting mechanism showing that it can operate on Calabi-Yau
manifolds where the new correction is present and dominated by the 4-cycle
controlling the overall volume if the volume is stabilised at values
$\mathcal{V} \gtrsim 10^3$. We discuss the phenomenological implication of
these bounds on $\mathcal{V}$ in the various scenarios.
