Nuclear matter at high density requires a relativistic description. Recent two-loop calculations in local quantum field theory models at finite density yield disastrously large contributions. We argue that the composite structure of nucleons ought to soften these contributions. This argument is supported by a model calculation in which we find very strong reductions in the Lamb shift and vacuum fluctuation contributions. At nuclear matter densities and beyond, the total-loop result is perturbatively small in comparison to the one-loop calculation.