  Working in the context of the CMSSM, we argue that phenomenological
constraints now require the universal soft supersymmetry-breaking scalar mass
m_0 be non-zero at the input GUT scale. This conclusion is primarily imposed by
the LEP lower limit on the Higgs mass and the requirement that the lightest
supersymmetric particle not be charged. We find that m_0 > 0 for all tan beta
if mu < 0, and m_0 = 0 may be allowed for mu > 0 only when tan beta sim 8 and
one allows an uncertainty of 3+ GeV in the theoretical calculation of the Higgs
mass. Upper limits on flavour-changing neutral interactions in the MSSM squark
sector allow substantial violations of non-universality in the m_0 values, even
if their magnitudes are comparable to the lower limit we find in the CMSSM.
Also, we show that our lower limit on m_0 at the GUT scale in the CMSSM is
compatible with the no-scale boundary condition m_0 = 0 at the Planck scale.
