Abstract. We discuss constraints on the internal volume size in type IIB string theory in the Large Volume Scenario, in the presence of various uplift terms. We then show how all the Kaehler moduli in type IIB string theory compactifications on generic Swiss Cheese type Calabi-Yau spaces may be stabilized by taking into account the F4 corrections to the potential recently discussed by Ciupke et al. The argument works for either sign of the Euler character. This extends the validity of LVS phenomenology well beyond the original framework. Finally we show how theoretically and observationally viable Fibre Inflation models can be obtained by including also one-loop string contributions.