Flexibly adjusting one's behavior depending on the task at hand is a hallmark of executive function. In two experiments, we explored pigeons' cognitive flexibility to concurrently perform two complex categorization tasks: a numerosity discrimination (where number was the relevant dimension and variability was the irrelevant dimension) and a variability discrimination (where variability was the relevant dimension and number was the irrelevant dimension). The flexibility of pigeons' behavior was evidenced by their rapid, on-demand switching between tasks within training sessions. In addition, in Experiment 1, pigeons more accurately performed the numerosity task with arrays of different stimuli than with arrays of same stimuli and they more accurately performed the variability task with arrays of 16 stimuli than with arrays of 6 stimuli. In Experiment 2, when the magnitudes of the relevant and irrelevant dimensions were congruent, pigeons' accuracy was higher than when the magnitudes were incongruent. Thus, the irrelevant dimension facilitated target discrimination performance when its magnitude matched the magnitude of the correct choice. These cross-task interactions suggest that a common computational mechanism underlies both discriminations. Pigeons' cognitive complexity and flexibility-even in the absence of a prefrontal cortex-indicates that other avian brain areas can support behaviors emblematic of executive functioning.