  We analyze minimal supersymmetric models in order to determine in what
parameter regions with what amount of fine-tuning they are capable of
accomodating the LHC-allowed top-stop degeneracy window. The stops must be
light enough to enable Higgs naturalness yet heavy enough to induce a 125 GeV
Higgs boson mass. These two constraints imply a large mass splitting. By an
elaborate scan of the parameter space, we show that stop-on-top scenario
requires at least Delta_CMSSM ~ O(10^4) fine-tuning in the CMSSM. By relaxing
the CMSSM parameter space with nonuniversal Higgs masses, we find that
Delta_NUHM1 ~ O(10^4). The CMSSM with gravitino LSP works slightly better than
the NUHM1 model. Compared to all these, the CMSSM with mu<0 and nonuniversal
gauginos yield a much smaller fine-tuning Delta_{mu,g} ~ O(100). Our results
show that gaugino sector can pave the road towards a more natural stop-on-top
scenario.
