Competition for fresh water between native and introduced plants is one important challenge facing native forests as rainfall variability increases. Competition can be especially acute for vegetation on Pacific atolls, which depend upon consistent rainfall to replenish shallow groundwater stores. Patterns of sap flow, water use, and diameter growth of Pisonia grandis trees were investigated on Sand Islet, Palmyra Atoll, Line Islands, during a period of low rainfall. Sap flow in the outer sapwood was reduced by 53% for P. grandis trees growing within coconut palm (Cocos nucifera) stands (n = 9) versus away from coconut palm (n = 9). This suggested that water uptake was being limited by coconut palm. Radial patterns of sap flow into the sapwood of P. grandis also differed between stands with and without coconut palm, such that individual tree water use for P. grandis ranged from 14 to 67 L day−1, averaging 47·8 L day−1 without coconut palm and 23·6 L day−1 with coconut palm. Diameter growth of P. grandis was measured from nine islets. In contrast to sap flow, competition with coconut palm increased diameter growth by 89%, equating to an individual tree basal area increment of 5·4 versus 10·3 mm2 day−1. Greater diameter growth countered by lower rates of water use by P. grandis trees growing in competition with coconut palm suggests that stem swell may be associated with water storage when positioned in the understory of coconut palm, and may facilitate survival when water becomes limiting until too much shading overwhelms P. grandis. Copyright © 2015 John Wiley & Sons, Ltd.