Water availability is a major factor limiting plant productivity in both natural and agronomic systems. Identifying putative drought resistance traits in crops and their wild relatives may be useful for improving crops grown under water-limiting conditions. Here we tested the expectation that a desert-dwelling sunflower species Helianthus niveus ssp. tephrodes (TEPH) would exhibit root and leaf traits consistent with greater ability to avoid drought than cultivated sunflower H. annuus (ANN) in a common garden environment. We compared TEPH and ANN at both the seedling and mature stages under well-watered greenhouse conditions. For traits assessed at the seedling stage TEPH required a longer time to reach a rooting depth of 30 cm than ANN and the two species did not differ in root:total biomass ratio at 30 cm rooting depth contrary to expectations. For traits assessed at the mature stage TEPH had a higher instantaneous water use efficiency and photosynthetic rate on a leaf area basis but a lower photosynthetic rate on a mass basis than ANN likely due to TEPH having thicker denser leaves. Contrary to expectations ANN and TEPH did not differ in leaf instantaneous stomatal conductance integrated water-use efficiency estimated from carbon isotope ratio or nitrogen concentration. However at both the seedling and mature stages TEPH exhibited a lower normalized difference vegetative index than ANN likely due to the presence of dense leaf pubescence that could reduce heat load and transpirational water loss under drought conditions. Thus although TEPH root growth and biomass allocation traits under well-watered conditions do not appear to be promising for improvement of cultivated sunflower TEPH leaf pubescence may be promising for breeding for drought-prone high radiation environments.