We describe an experiment designed to distinguish between two models of risk-sensitive feeding behaviour: the variance discounting model and the z-score model. The variance discounting model assumes that mean reward levels do not affect preferences over reward variability, but the z-score model assumes that mean reward levels do affect preferences over variability. We presented two choices to feeding rufous hummingibrds, Selaphoruous rufus. One alternative had a higher mean and a higher variance than the other. After measuring preference, we increased the mean of both alternatives by adding the same amount to all possible outcomes. The variance discounting model predicts that such a general shift should not change preferences, but the z-score model predicts that preferences will change. Our results support the z-score model. The variance discounting model's assumption of constant risk-aversion fails.