We perform a global fit to Higgs signal-strength data in the context of light stops in Natural SUSY. In this case, the Wilson coefficients of the higher dimensional operators mediating g g → h and h → γ γ, given by c g , c γ , are related by c g = 3 (1 + 3 α s /(2 π))c γ /8. We examine this predictive scenario in detail, combining Higgs signalstrength constraints with recent precision measurements of m W , Br(B → X s γ) constraints and direct collider bounds on weak scale SUSY, finding regions of parameter space that are consistent with all of these constraints. However it is challenging for the allowed parameter space to reproduce the observed Higgs mass value with sub-TeV stops. We discuss some of the direct stop discovery prospects and show how Higgs search data can be used to exclude light stop parameter space difficult to probe by direct collider searches. We determine the current status of such indirect exclusions and estimate their reach by the end of the 8 TeV LHC run.