  The Standard Model (SM) predictions for the hadronic electric dipole moments
(EDMs) are well far from the present experimental resolutions, thus, the EDMs
represent very clean probes of New Physics (NP) effects. Especially, within an
MSSM framework with flavor-changing (but not necessarily CP violating) soft
terms, large and potentially visible effects to the EDMs are typically
expected. In this Letter we point out that, beyond-leading-order (BLO) effects,
so far neglected in the literature, dominate over the leading-order (LO)
effects in large regions of the parameter space, hence, their inclusion in the
evaluation of the hadronic EDMs is unavoidable.
