Precise knowledge of the thermodynamic properties of zero-temperature, high-density quark matter (QM) can constrain the neutron-star-matter equation of state (EOS), even at much lower densities. However, current bounds on this QM EOS suffer from rather large uncertainties stemming from renormalization-scale dependence. In this talk, I will lay out how to improve the dense QM EOS beyond N2LO, and how to disentangle contributions to the pressure at N3LO. At this higher order, interactions involving the dynamically screened, long-wavelength (soft) gluon modes in loop corrections can contribute. I will present the fully soft contribution to the pressure stemming from self-interactions between these long-wavelength, screened gluons. This soft sector is well-behaved at high density, contrary to the case encountered at high temperatures, and this new contribution slightly decreases the renormalization-scale dependence of the EOS at high density.