We study the Tevatron search potential for minimal supergravity (mSUGRA) and find two observables which reveal complementary information on the mSUGRA parameter space: the “gold-plated” decays of charginos/neutralinos to trilepton final states and the rare decay Bs → μ+μ− . For the universal gaugino mass, M1/2 below 250 GeV and for the universal scalar fermion mass, M0 outside of 200-370 GeV we face a “nolose” situation for the Tevatron: If tan <∼ 30, the Tevatron has a chance to see the trilepton events but not Bs → μ+μ− during Run IIa, whereas for larger tan the trilepton events become invisible (at least with an integrated luminosity of 2 fb−1) while Bs → μ+μ− is enhanced to an observable level. For this study we perform an updated analysis of the trilepton signature which includes the full set of the decay matrix elements and spin correlations. This leads to a new, more promising search reach for the Tevatron. 1