  We discuss electric dipole moments (EDMs) in the framework of CP-violating
natural supersymmetry (SUSY). Recent experimental results have significantly
tightened constraints on the EDMs of electrons and of mercury, and substantial
further progress is expected in the near future. We assess how these results
constrain the parameter space of natural SUSY. In addition to our discussion of
SUSY, we provide a set of general formulas for two-loop fermion EDMs, which can
be applied to a wide range of models of new physics. In the SUSY context, the
two-loop effects of stops and charginos respectively constrain the phases of
$A_t \mu$ and $M_2 \mu$ to be small in the natural part of parameter space. If
the Higgs mass is lifted to 125 GeV by a new tree-level superpotential
interaction and soft term with CP-violating phases, significant EDMs can arise
from the two-loop effects of $W$ bosons and tops. We compare the bounds arising
from EDMs to those from other probes of new physics including colliders, $b \to
s \gamma$, and dark matter searches. Importantly, improvements in reach not
only constrain higher masses, but require the phases to be significantly
smaller in the natural parameter space at low mass. The required smallness of
phases sharpens the CP problem of natural SUSY model building.
