  In this paper, the flavor structure of quark and lepton EDMs in the SM and
beyond is investigated using tools inspired from Minimal Flavor Violation.
While Jarlskog-like flavor invariants are adequate for estimating CP-violation
from closed fermion loops, non-invariant structures arise from rainbow-like
processes. Our goal is to systematically construct these latter flavor
structures in the quark and lepton sectors, assuming different mechanisms for
generating neutrino masses. Numerically, they are found typically much larger,
and not necessarily correlated with, Jarlskog-like invariants. Finally, the
formalism is adapted to deal with a third class of flavor structures, sensitive
to the flavored U(1) phases, and used to study the impact of the strong
CP-violating interaction and the interplay between the neutrino Majorana phases
and possible baryon and/or lepton number violating interactions.
