  Soft supersymmetry-breaking terms provide a wealth of new potential sources
of flavour violation, which are tightly constrained by precision experiments.
This has posed a challenge to construct flavour models which both explain the
structure of the Standard Model Yukawa couplings and also predict soft-breaking
patterns that are compatible with these constraints. While such models have
been studied in great detail, the impact of flavour violating soft terms on the
Higgs mass at the two-loop level has been assumed to be small or negligible. In
this letter, we show that large flavour violation in the up-squark sector can
give a positive or negative mass shift to the SM-like Higgs of several GeV,
without being in conflict with other observations. We investigate in which
regions of the parameter space these effects can be expected.
