We analyze minimal supersymmetric models in order to determine in what parameter regions with what amount of fine-tuning they are capable of accommodating 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 the stop-on-top scenario requires at least fine-tuning in the constrained minimal supersymmetric Standard Model (CMSSM). By relaxing the CMSSM parameter space with nonuniversal Higgs masses, we find that . The CMSSM with a gravitino lightest supersymmetric particle works slightly better than the nonuniversal Higgs mass model. Compared to all these, the CMSSM with and nonuniversal gauginos yields a much smaller fine-tuning . Our results show that the gaugino sector can pave the road toward a more natural stop-on-top scenario.