  We revisit the proposal that the resolution of the Cosmological Constant
Problem involves a sub-millimeter breakdown of the point-particle approximation
for gravitons. No fundamental description of such a breakdown, which
simultaneously preserves the point-particle nature of matter particles, is yet
known. However, basic aspects of the self-consistency of the idea, such as
preservation of the macroscopic Equivalence Principle while satisfying quantum
naturalness of the cosmological constant, are addressed in this paper within a
Soft Graviton Effective Theory. It builds on Weinberg's analysis of soft
graviton couplings and standard heavy particle effective theory, and minimally
encompasses the experimental regime of soft gravity coupled to hard matter. A
qualitatively distinct signature for short-distance tests of gravity is
discussed, bounded by naturalness to appear above approximately 20 microns.
