  We show how the spectrum of the minimal anomaly-mediated supersymmetry
breaking model can be constrained from the condition that the electroweak
symmetry breaking minimum of the scalar potential is the deepest point in the
field space. Applying the current experimental bounds and scanning over the
whole parameter space, we rule out selectrons below 378 GeV and staus below 269
GeV, the numbers having a modest uncertainty. We also find a new upper bound on
the wino-like chargino mass for a given slepton mass. This rules out the
possibility of slepton pair production at ongoing or upcoming colliders like
the Tevatron or the Next Linear Collider at $\sqrt{s}=500$ GeV, where pair
production of charginos may be the only available signal.
