  We study the contributions of supersymmetric models with a $U(1)$ horizontal
symmetry and only spontaneous CP breaking to various lepton flavor observables,
such as $\mu \to e\gamma$ and the electron electric dipole moment. We show that
both a horizontal symmetry and a lack of explicit CP violation can alleviate
the existing bounds from such observables. The undetermined $\mathcal{O}(1)$
coefficients in such mass matrix models muddle the interpretation of the bounds
from various flavor observables. To overcome this, we define a new fine-tuning
measure for different observables in such setups. This allows us to study how
naturally the observed IR flavor observables can emerge from a given mass
matrix model. We use our flavor-naturalness measure in study of our
supersymmetric models and quantify the degree of fine tuning required by the
bounds from various lepton flavor observables at each mass scale of sleptons,
neutralinos, and charginos. We also comment on implications of the observed
discrepancy in the anomalous magnetic moment of the muon for our supersymmetric
models.
