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.