The argument is currently made that hunting seriously compromises the welfare of the hunted animal, in a way that is morally unacceptable. The paper presents a theory of animal minds, and a theory of our duties of care towards members of other species. It goes on to examine what is meant by compromising welfare, discusses the crucial concept of stress as this concept features in animal welfare science, and explores the conditions under which stress becomes distress. The argument moves towards the conclusion that there are conditions under which distress inflicted by a human being is morally unacceptable, but that these conditions are not met by the normal methods of hunting with hounds, even though they are frequently met by shooting and trapping.