The hierarchy problem is the main hint of new physics at the TeV scale, supersymmetry and composite Higgs models being two of the big classes of solutions. Several analyses have been performed at the LHC in the search for signals of these models, will null results so far. In this article we argue that $(i)$ current searches have only explored small regions of the parameter space of these models, $(ii)$ these regions are often less motivated than others not yet explored, $(iii)$ in either case, current constraints do not necessarily put naturalness under pressure. We also extend this discussion to searches for models of neutrino masses.