ℤ2 × ℤ2 Coxeter orbifolds are constructed with the property that some twisted sectors have fixed planes for which the six-torus cannot be decomposed into a direct sum T2 ⊕ T4 with the fixed plane lying in T2. The string loop threshold corrections to the gauge coupling constants are derived, and display symmetry groups for the T and U moduli that are subgroups of the full modular group PSL(2, ℤ). The effective potential for duality invariant gaugino condensate in the presence of hidden sector matter is constructed and minimized for the values of the moduli. The effect of Wilson lines on the modular symmetries is also studied.