  We present, in the context of the Minimal Supersymmetric Standard Model, a
detailed one-loop analytic study of the minimization conditions of the
effective potential in the Higgs sector.
  Special emphasis is put on the role played by $Str M^4$ in the determination
of the electroweak symmetry breaking conditions, where first and second order
derivatives of the effective potential are systematically taken into account.
Novel, necessary (and sufficient in the Higgs sector) model-independent
constraints, are thus obtained analytically, leading to new theoretical lower
and upper bounds on $\tan \beta$. Although fully model-independent, these
bounds are found to be much more restrictive than the existing model-dependent
ones! A first illustration is given in the context of a SUGRA-GUT motivated
scenario.
