Taking a bottom-up point of view and focussing on the lack of signals so far in the Higgs and in the flavour sectors, we argue in favour of giving consideration to supersymmetric extensions of the Standard Model where the lightest Higgs boson has a mass between 200 and 300 GeV and the first two generations of s-fermions are above 20 TeV. After examining the simplest extensions of the Minimal Supersymmetric Standard Model that allow this in a natural way, we summarize the main consequences of this pattern of masses at the LHC and we analyze the consequences of a heavier than normal Higgs boson for Dark Matter.