The requirement that SUSY should solve the hierarchy problem without undue fine-tuning imposes severe constraints on the new supersymmetric states. With the MSSM spectrum and soft SUSY breaking originating from universal scalar and gaugino masses at the Grand Unification scale, we show that the low-fine-tuned regions fall into two classes that will require complementary collider and dark matter searches to explore in the near future. The first class has relatively light gluinos or squarks which should be found by the LHC in its first run. We identify the multijet plus E T miss signal as the optimal channel and determine the discovery potential in the first run. The second class has heavier gluinos and squarks but the LSP has a significant Higgsino component and should be seen by the next generation of direct dark matter detection experiments. The combined information from the 7 TeV LHC run and the next generation of direct detection experiments can test almost all of the CMSSM parameter space consistent with dark matter and EW constraints, corresponding to a fine-tuning not worse than 1: 100. To cover the complete low-fine-tuned region by SUSY searches at the LHC will require running at the full 14 TeV CM energy; in addition it may be tested indirectly by Higgs searches covering the mass range below 120 GeV.