[en] We analyse a new N=1 string tree level correction at O(α'²) to the Kaehler potential of the volume moduli of type IIB Calabi-Yau flux compactification found recently by T. W. Grimm, R. Savelli and M. Weissenbacher (arXiv:1303.3317 [hep-th]) 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 vertical stroke W₀ vertical stroke < or similar 10^-3, while parametrically controlled survival of the KKLT minimum needs extreme tuning of W₀ close to zero. We also analyse the Kaehler 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 V>or similar 10³. We discuss the phenomenological implication of these bounds on V in the various scenarios.