Recent discoveries of higher cognitive abilities in some species of birds and mammals are bringing about radical changes in our attitudes to animals and will lead to changes in legislation for the protection of animals. We fully support these developments, but at the same time we recognize that the scientific study of higher cognition in animals has touched on only a small number of vertebrate species. Accordingly, we warn that calls to extend rights, or to at least better welfare protection, for the handful of species that have revealed their intelligence to us may be counterproductive. While this would improve the treatment of the selected few, be they birds or mammals, a vast majority of species, even closely related ones, will be left out. This may not be a particular problem if being left out is only a temporary state that can be changed as new information becomes available. But, in practice, those protected and not protected are separated by a barrier that can be more difficult to remove than it was to erect in the first place. We summarize the recent research on higher cognition from the position of active researchers in animal behavior and neuroscience.