In a supersymmetric theory, the IR contributions to the Higgs mass are calculable below the mediation scale Λ_{UV} in terms of the IR field content and parameters. However, logarithmic sensitivity to physics at Λ_{UV} remains. In this Letter, we present a first example of a framework, dictated by symmetries, to supersoften these logarithms from the matter sector. The result is a model with finite, IR-calculable corrections to the Higgs mass. This requires the introduction of new fields-the "lumberjacks"-whose role is to screen the UV-sensitive logs. These models have considerably reduced fine-tuning, by more than an order of magnitude for high-scale supersymmetry. This impacts interpretations of the natural parameter space, suggesting it may be premature to declare a naturalness crisis for high-scale supersymmetry.