  We demonstrate that in effective theories arising from a class of N=1
fluxless compactifications of M-theory on a G2 manifold with low energy
supersymmetry, CP-violating phases do not appear in the soft-breaking
Lagrangian except via the Yukawas appearing in the trilinear parameters. Such a
mechanism may be present in other string compactifications as well; we describe
properties sufficient for this to occur. CP violation is generated via the
Yukawas since the soft trilinear matrices are generically not proportional to
the Yukawa matrices. Within the framework considered, the estimated theoretical
upper bounds for electric dipole moments (EDM) of the electron, neutron and
mercury are all within the current experimental limits and could be probed in
the near future.
