  In a supersymmetric (SUSY) theory, the IR-contributions to the Higgs mass are
calculable below the mediation scale $\Lambda_{\text{UV}}$ in terms of the IR
field content and parameters. However, logarithmic sensitivity to physics at
$\Lambda_{\text{UV}}$ remains. In this work 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 SUSY.
