Centrifuging experiments on olivine, chromite, and plagioclase aggregates saturated in basaltic liquid show evidence of viscous compaction. The compaction profiles are inconsistent with the porosity-dependence of current macroscopic compaction models. We eliminate this inconsistency by adopting the porosity-dependence derived from microscopic models for a matrix that compacts by grain-boundary diffusion-controlled creep. The time to halve the porosity of natural olivine igneous sediments by compaction is estimated from the centrifuging experiments to be O(10³)y. Half-times for plagioclase and chromite layers are O(10⁴-10⁵)y, suggesting that such layers compact on magmatic time scales only if they are loaded by additional sedimentation. At conditions relevant to melt flow in asthenospheric settings and trans-crustal magmatic systems, the bulk and shear viscosities inferred for olivine and plagioclase are O(10¹⁷)Pa-s and imply time- and length-scales for viscous compaction that are substantially shorter than anticipated from earlier experimental studies. Our analysis serendipitously reveals that the oft-neglected solidity term of the Carman-Kozeny porosity-permeability relation is essential to prevent non-physical behavior in models of cumulate compaction.