  Light states associated with the hierarchy problem affect the Higgs LHC
production and decays. We illustrate this within the MSSM and two simple
extensions applying the latest bounds from LHC Higgs searches. Large deviations
in the Higgs properties are expected in a natural SUSY spectrum. The discovery
of a non-Standard-Model Higgs may signal the presence of light stops accessible
at the LHC. Conversely, the more the Higgs is Standard-Model-like, the more
tuned the theory becomes. Taking the ratio of different Higgs decay channels at
the LHC cancels the leading QCD uncertainties and potentially improves the
accuracy in Higgs coupling measurements to the percent level. This may lead to
the possibility of doing precision Higgs physics at the LHC. Finally, we
entertain the possibility that the ATLAS excess around 125 GeV persists with a
Higgs production cross-section that is enhanced compared to the SM. This
increase can only be accommodated in extensions of the MSSM and it may suggest
that stops lie below 400 GeV, likely within reach of next year's LHC run.
