  We use the combined action of Z_2-chiral reflections (T-dualities) and shifts
to build N=1,2 supersymmetric four-dimensional string compactifications with
few moduli. In particular, we consider Z_2^4 asymmetric orbifolds of Type IIB
on the maximal torus of SO(12) that mimic N=2 Calabi-Yau compactifications with
small "effective" Hodge numbers starting from (h_{11}, h_{21})=(1,1). We
analyze possible unoriented projections, providing Type I examples with or
without open strings. N=1 oriented asymmetric shift-orbifolds of Type IIB with
few chiral multiplets are also presented.
