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Desertification, the conversion of arid grasslands to shrublands due to overgrazing and drought, is occurring on over a quarter of the land on earth. Conceptual models of desertification predict desertified shrublands are in a stable state, and grass recovery is unlikely. These models hypothesize that as grass is lost, feedback loops involving low soil nutrients or insufficient water infiltration rates prevent the return of perennial grasses to desertified sites. However, these models cannot account for recent reports of reversals of desertification following long-term livestock removal. Here, we analyzed soil nutrients and water infiltration at a desertified site where native perennial grasses are recovering inside a 49-year livestock exclosure. We found higher water infiltration and soil nutrients inside the exclosure. We postulate that in the absence of livestock there is a slow release from compaction that, over decades, results in an increase in water infiltration and a concomitant decrease in erosion, which promotes nutrient accumulation in the soil. Our data support key desertification model assumptions: increased nutrients and infiltration are associated with reversal of desertification. This suggests that given sufficient time and removal of livestock, soil properties at some desertified sites can improve sufficiently to support the re-establishment of perennial grasses.