Woody plant effects on grass production at specific points in some rangeland savannas may be a function of numerous surrounding woody plants with lateral roots that extend into those patches of grass. This study determined the effects of increasing zones of honey mesquite (Prosopis glandulosa Torr.) influence on the production of three perennial grass types (C₄ shortgrasses, C₃ midgrasses, and C₄ midgrasses) at specific points in gaps between mesquite trees in each of five years. Mesquite canopy cover was determined by geospatial analysis of aerial images for progressively increasing zones (0–5, 0–10, 0–15, and 0–20 m radius) surrounding each grass production point. The woody cover/grass production relationships were mostly linear for C₄ shortgrasses and C₃ midgrasses, and mostly a declining exponential curve for C₄ midgrasses in all canopy zones, indicating that C₄ midgrasses were most sensitive to increasing mesquite cover, especially at covers >30%. The relationship between mesquite cover and C₄ shortgrass production was strongest (i.e., highest r²) when the smallest woody cover zones (0–5 and 0–10 m) were included. In contrast, the relationship between cover and C₄ midgrass production was strongest when the largest zones (0–15 and 0–20 m) were included. These differences were attributed to an inability of C₄ midgrasses to persist in smaller intercanopy gaps resulting from increases in mesquite density and infilling. Annual precipitation and C₃ annual grass invasions played a large role in determining the woody cover/grass production relationship for each grass type. This study illustrates the complexity involved in quantifying woody cover/grass production relationships in savanna ecosystems. Maintaining productive stands of C₄ midgrasses may be facilitated by maintaining woody cover below 30% threshold levels and possibly by limiting grazing during episodic high rainfall events in midsummer when this grass type becomes somewhat decoupled from woody cover effects.