Combining production of low-input alternative crops together with cotton (Gossypium hirsutumL.) under deficit irrigation (DI) has gained attention for purposes of rotation, diversification, and saving water resources in West Texas. The objective of this study was to determine a relationship between water extraction patterns and water use efficiency (WUE) of crops tolerant of the semiarid conditions in West Texas. Irrigation responses of cotton, sesame (Sesamum indicum L.), and grain sorghum [Sorghum bicolor (L.) Moench] were compared in 2017 and 2018 at irrigation levels ranging from extreme DI to mild DI based on crop yield, aboveground biomass, water extraction patterns, and WUE. Cotton and sorghum biomass production and yield increased with irrigation rate, whereas sesame productivity was not significantly increased in either year. The water extraction patterns suggested that the rooting system of sesame was not as extensive compared with cotton and sorghum and did not change substantially among irrigation treatments, and sesame yields did not significantly vary among DI treatments. The implication is that the biomass production and yield of sesame, even under low irrigation management, was not water limited, even in irrigation treatments that resulted in 25% yield losses in sorghum and 40% yield losses in cotton. As a result, the WUE of sesame was dramatically decreased with additional irrigation, whereas cotton and sorghum maintained similar WUE under all irrigation treatments. Therefore, water-limiting environments may not actually be water limiting to sesame, and the bigger limitation is the yield potential associated with a baseline irrigation level far below that of cotton or sorghum.