  The minimal supersymmetric standard model (MSSM) with complex parameters can
contribute sizably to muon/electron anomalous magnetic dipole momemnt ($g-2$)
and electric dipole moment (EDM). The electron $g-2$ interplays with electron
EDM; the muon $g-2$ can also interplay with electron EDM assuming the
universality between smuon and selectron masses, either of which can constrain
the relevant CP-phases in the MSSM.
  In this work, we first use such an interplay to derive an approximate
analytical upper limit on the relevant CP-phase. Then we extensively scan the
parameter space to obtain more accurate upper limits. We obtain the following
observations:
  (i) The muon $g-2$ in the $2\sigma$ range combined with the electron EDM
upper limit (assuming the universality between smuon and selectron masses)
typically constrains the relevant CP-phase under $1.9\times 10^{-5}
(\text{rad})$;
  (ii) The electron $g-2$ in the $2\sigma$ range (Berkeley) interplays with the
electron EDM upper limit (without assuming the universality between smuon and
selectron masses) constrains the relevant CP-phase under $3.9\times
10^{-6}(\text{rad})$ (also requiring muon $g-2$ in the allowed $2\sigma$
range). We also find some special cancellations in the parameter space which
can relax the constraints by a couple of orders.
  Such stringent limits on CP-phases may pose a challenge for model building of
SUSY, i.e., how to naturally suppress these phases.
