Indirect utilitarianism, proposed as a promising alternative to act or direct utilitarianism which has long been criticized as being self-defeating and counterintuitive, is often taken to have enough flexibility to incorporate intuitive moral principles and substantive human rights into a utilitarian moral theory. This flexibility of indirect utilitarianism, however, has provoked much doubt regarding its identity as a kind of utilitarianism. As a representative scholar who raised this doubt, Bernard William declares that it is direct utilitarianism that speaks for "the spirit of utilitarianism," and points out that the distinction between direct and indirect utilitarianism is not so clear in the sense that both are supposed to be "the systems of total assessment." In this paper, accommodating partly what Bernard Williams points out, I shall critically examine that hypothesis of the two stages ― 'critical' and 'practical' stages ― of moral thinking which indirect utilitarianism typically admits. According to this hypothesis, the principle of utility operates not as a practical decision-making procedure but only as a criterion of rightness or, as I shall call it, "background rationale." Confining the role of the principle of utility to this background rationale, indirect utilitarianism seems to degrade utilitarianism as an 'esoteric' morality. Here with John Rawl's concept of "publicity condition," I shall claim that a truly utilitarian theory cannot be an esoteric morality and, if it is, it will lose its qualification to be a competing public moral basis of society. This is not at all a trivial loss and thus, as I shall conclude, indirect utilitarian strategy is not in the best interest of utilitarianism per se.