  We discuss the consequences of relaxing the Minimal Flavour Violation
assumption in the up-squark sector on the phenomenology of SUSY models. We
study the impact of the off-diagonal entries in the soft SUSY-breaking matrices
on the mass of the lightest Higgs scalar and we derive the approximate
analytical formulae that quantify this effect. We show that $m_h$ can be
enhanced by up to 13-14 GeV in the case of the phenomenological MSSM with the
inverted hierarchy of masses in the squark sector and zero stop mixing, and up
to 4-5 GeV in GUT-constrained scenarios where the magnitude of the enhancement
is mitigated by renormalization group effects. We also perform a global
analysis of an inverted hierarchy GFV scenario, taking into account the
experimental bounds from the measurements of relic density, EW precision
observables and B-physics. We show that the allowed parameter space of the
model is strongly constrained by $m_W$, $\sin^2\theta_{eff}$ and $BR(B_s \to
\mu^+\mu^-)$, requiring $m_0(3)$<1500 GeV and $m_{1/2}$<1800 GeV, as well as a
large non-zero (2,3) entry in the up-squark trilinear matrix.
