  The experiments at the Large Hadron Collider (LHC) have pushed the limits on
masses of supersymmetric particles beyond the $\sim$TeV scale. This compromises
naturalness of the simplest supersymmetric extension of the Standard Model, the
minimal supersymmetric Standard Model (MSSM). In this paper we advocate that
perhaps the current experimental data are actually hinting towards the physics
beyond MSSM. To illustrate this, we treat MSSM as a low energy limit of a more
fundamental yet unspecified theory at a scale $\Lambda$, and compute the
fine-tuning measure $\Delta$ for generic boundary conditions on soft SUSY
breaking parameters and various cut-off scales. As a general trend we observe
reduction in fine-tuning together with lowering $\Lambda$. In particular,
perfectly natural [$\Delta \lesssim \mathcal{O}(10)$] theories with a multi-TeV
spectrum of supersymmetric particles and consistent with all current
observations can be obtained for $\Lambda \sim \mathcal{O}(100)$TeV. The
lowering of the fine-tuning for large cut-off scales can also be observed in
theories exhibiting special quasi-fixed point behaviours of parameters. Our
observations call for a more throughout exploration of possible alternative
ultraviolet completions of MSSM.
