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The minimal supersymmetric standard model (MSSM) with complex parameters cancontribute sizably to muon/electron anomalous magnetic dipole momemnt ($g-2$)and electric dipole moment (EDM). The electron $g-2$ interplays with electronEDM; the muon $g-2$ can also interplay with electron EDM assuming theuniversality between smuon and selectron masses, either of which can constrainthe relevant CP-phases in the MSSM.  In this work, we first use such an interplay to derive an approximateanalytical upper limit on the relevant CP-phase. Then we extensively scan theparameter space to obtain more accurate upper limits. We obtain the followingobservations:  (i) The muon $g-2$ in the $2\sigma$ range combined with the electron EDMupper 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 theelectron EDM upper limit (without assuming the universality between smuon andselectron masses) constrains the relevant CP-phase under $3.9\times10^{-6}(\text{rad})$ (also requiring muon $g-2$ in the allowed $2\sigma$range). We also find some special cancellations in the parameter space whichcan relax the constraints by a couple of orders.  Such stringent limits on CP-phases may pose a challenge for model building ofSUSY, i.e., how to naturally suppress these phases.

Constraining CP-phases in SUSY: an interplay of muon/electron $g-2$ and electron EDM