  We present a fit to the 2012 LHC Higgs data in different supersymmetric
frameworks using naturalness as a guiding principle. We consider the MSSM and
its D-term and F-term extensions that can raise the tree-level Higgs mass. When
adding an extra chiral superfield to the MSSM, three parameters are needed
determine the tree-level couplings of the lightest Higgs. Two more parameters
cover the most relevant loop corrections, that affect the h\gamma\gamma and hgg
vertexes. Motivated by this consideration, we present the results of a five
parameters fit encompassing a vast class of complete supersymmetric theories.
We find meaningful bounds on singlet mixing and on the mass of the pseudoscalar
Higgs mA as a function of tan\beta\ in the MSSM. We show that in the (mA,
tan\beta) plane, Higgs couplings measurements are probing areas of parameter
space currently inaccessible to direct searches. We also consider separately
the two cases in which only loop effects or only tree-level effects are
sizeable. In the former case we study in detail stops' and charginos'
contributions to Higgs couplings, while in the latter we show that the data
point to the decoupling limit of the Higgs sector. In a particular realization
of the decoupling limit, with an approximate PQ symmetry, we obtain constraints
on the heavy scalar Higgs mass in a general type-II Two Higgs Doublet Model.
