Humans and other animals often find it difficult to choose a delayed reward over an immediate one, even when the delay leads to increased pay-offs. Using a visible incremental reward procedure, we tested the ability of three grey parrots to maintain delay of gratification for an increasingly valuable food pay-off. Up to five sunflower seeds were placed within the parrot’s reach, one at a time, at a rate of one seed per second. When the parrot took a seed the trial was ended and the birds consumed the accumulated seeds. Parrots were first tested in daily sessions of ten trials and then with single daily trials. For multiple trial sessions, all three parrots showed some limited improvement across 30 sessions. For single trial sessions, only one parrot showed any increase in seed acquisition across trials. This parrot was also able to consistently obtain two or more seeds per trial (across both multiple and single trial conditions) but was unable to able to wait 5 s to obtain the maximum number of seeds. This parrot was also tested on a slower rate of seed presentation, and this significantly reduced her mean seed acquisition in both multiple and single trial conditions, suggesting that both value of reward available and delay duration impact upon self-control. Further manipulation of both the visibility and proximity of seeds during delay maintenance had little impact upon tolerance of delays for both parrots tested in this condition. This task demanded not just a choice of delayed reward but the maintenance of delayed gratification and was clearly difficult for the parrots to learn; additional training or alternative paradigms are required to better understand the capacity for self-control in this and other species.