Many arid grasslands have been desertified over the past two centuries as perennial grass cover has declined and shrub cover has increased. Theoretical models and empirical work suggests that restoration of desertified grasslands will be difficult due to a positive feedback between grass cover and water infiltration rate: reductions in grass cover are postulated to reduce water infiltration rates below a threshold necessary for grass establishment thus facilitating shrubs over grasses which results in a stable desertified state. Recently, however, there have been independent reports of the reversal of desertification following long-term livestock removal. We suggest a novel mechanism to account for these observations: the natural reduction in soil compaction following long-term livestock removal and associated changes in water infiltration rate. We evaluate this hypothesis by comparing vegetation, water infiltration and soil compaction at three nearby livestock exclosures that differ in time since livestock removal. Across sites, relative differences (values on opposite sides of a grazing fence) in water infiltration rate and soil compaction increased with time since livestock removal and perennial grasses have increased significantly inside the oldest exclosure. Our work suggests that i) soil compaction is a missing element in models of desertification and ii) restoration of desertified grasslands may be possible given sufficient time for changes in soil properties.