  We analyze the 2011 LHC Higgs data in the context of simplified new physics
models addressing the naturalness problem. These models are expected to contain
new particles with sizable couplings to the Higgs boson, which can easily
modify the Higgs production cross sections and branching fractions. We focus on
searches in the Higgs to 4 leptons and Higgs to diphoton channels, in the
latter case including the vector boson fusion production mode. Combining the
available ATLAS and CMS data in these channels, we derive constraints on an
effective low-energy theory of the Higgs boson. We then map several simplified
scenarios to the effective theory, capturing numerous natural new physics
models such as supersymmetry and Little Higgs, and extract the constraints on
the corresponding parameter space. We show that simple models where one
fermionic or one scalar partner is responsible for stabilizing the Higgs
potential are already constrained in a non-trivial way by LHC Higgs data.
