The use of deficit irrigation (DI) management in growing crops tolerant of the semiarid conditions in West Texas may save irrigation without significant yield penalties. Field experiments were conducted at New Deal, TX, in 2017 and 2018 to determine the effects of four levels of DI (extreme, severe, moderate, and mild) on the seed yield, yield components, harvest index (HI), and oil content of three oilseed crops: sesame (Sesamum indicum L.), safflower (Carthamus tinctorius L.), and sunflower (Helianthus annuus L.). Combined irrigation and precipitation equivalent to 345 mm applied throughout the crop’s life cycle was sufficient to maintain growth and development without significant penalties to the yield, yield components, HI, and oil content of the crops. Seed yields ranged from 1241 to 1359 kg ha–1 in sesame, 1365 to 1676 kg ha–1 in safflower, and 1174 to 3367 kg ha–1 in sunflower. Oil content of sesame ranged from 50.1 to 52.3%, oil content of safflower ranged from 35.4 to 39.5%, and oil content of sunflower ranged from 24.0 to 46.8%. Heavy precipitation from vegetative to reproductive stage caused favorable conditions for pest proliferation and damage to sunflower, highlighting a possible pitfall due to its pest susceptibility. Results demonstrate that sesame, safflower, and sunflower are potential low-input oilseed crops that can grow under DI conditions without significant reductions to yield and oil content. In conjunction with economic evaluations, these results can be useful when developing or re-assessing guidelines for optimal agronomic practices involving non-traditional crops under reduced irrigation.