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Abstract Moduli stabilisation in superstring compactifications on Calabi-Yau orientifolds remains a key challenge in the search for realistic string vacua. In particular, odd moduli arising from the reduction of 2-forms (B 2 , C 2) in type IIB are largely unexplored despite their relevance for inflationary model building. This article provides novel insights into the general structure of 4D N $$ \mathcal{N} $$ = 1 F-term scalar potentials at higher orders in the α′ and g s expansion for arbitrary Hodge numbers. We systematically examine superpotential contributions with distinct moduli dependences which are induced by fluxes or non-perturbative effects. Initially, we prove the existence of a no-scale structure for odd moduli in the presence of (α′)3 corrections to the Kähler potential. By studying a partially SL(2, ℤ)-completed form of the Kähler potential, we derive the exact no-scale breaking effects at the closed string 1-loop and non-perturbative D-instanton level. These observations allow us to present rigorous expressions for the F-term scalar potential applicable to arbitrary numbers of moduli in type IIB Calabi-Yau orientifold compactifications. Finally, we compute the Hessian for odd moduli and discuss potential phenomenological implications.