Social status can have striking effects on health in humans and other animals, but the causes often are unknown. In male vertebrates, status-related differences in health may be influenced by correlates of male social status that suppress immune responses. Immunosuppressive correlates of low social status may include chronic social stress, poor physical condition, and old age; the immunosuppressive correlates of high status may include high testosterone and energetic costs of reproduction. Here we test whether these correlates could create status-related differences in immune function by measuring the incidence of illness and injury and then examining healing rates in a 27-y data set of natural injuries and illnesses in wild baboon males. We found no evidence that the high testosterone and intense reproductive effort associated with high rank suppress immune responses. Instead, high-ranking males were less likely to become ill, and they recovered more quickly than low-ranking males, even controlling for differences in age. Notably, alpha males, who experience high glucocorticoids, as well as the highest testosterone and reproductive effort, healed significantly faster than other males, even other high-ranking males. We discuss why alpha males seem to escape from the immunosuppressive costs of glucocorticoids but low-ranking males do not, including the idea that glucocorticoids' effects depend on an individual's physiological and social context.