  As SMEFT is a framework of growing importance to analyze high-energy data,
understanding its parameter space is crucial. The latter is commonly split into
CP-even and CP-odd parts, but this classification is obscured by the fact that
CP violation is actually a collective effect that is best captured by
considering flavor-invariant combinations of Lagrangian parameters. First we
show that fermion rephasing invariance imposes that several coefficients
associated to dimension-six operators can never interfere with operators of
dimension $\leq4$ and thus cannot appear in any physical observable at
$\order{1/\Lambda^2}$. For those that can, instead, we establish a one-to-one
correspondence with CP-odd flavor invariants, all linear with respect to SMEFT
coefficients. We explicitly present complete lists of such linear CP-odd
invariants, and carefully examine their relationship to CP breaking throughout
the parameter space of coefficients of dimension $\leq 4$. Requiring that these
invariants all vanish, together with the Jarlskog invariant, the strong-CP
phase, and the 6 CP-violating dimension-6 bosonic operators, provides
$699(+1+1+6)$ conditions for CP conservation to hold in any observable at
leading order, $\cO\(1/\Lambda^2\)$.
