We show that the quark flavour structure and CP violating phenomena are strongly correlated in supersymmetric theories. For a generic pattern of supersymmetry breaking the two broad categories of Yukawa couplings, democratic and hierarchical textures, have entirely different phenomenological implications. With hierarchical Yukawas, the rephasing invariant phase, arg(V_us V_cb V_cb^* V_cs^*), in the CKM mixing matrix has to be of order unity, while the SUSY CP violating phases are severely constrained by electric dipole moments, giving rise to the so-called SUSY CP problem. With democratic Yukawas, all experimental CP results can be accommodated with small values for the CKM and SUSY CP violating phases (i.e., CP can be considered as an approximate symmetry at the high energy scale). We also show that within this scenario, an entirely real CKM matrix in supersymmetric models is still allowed by the present experimental results.

16 pages, 6 eps figures