How Indirect Can Indirect Utilitarianism Be?

Most act-utilitarians now reject the direct utilitarianism of Bentham. They do so because they are convinced of what I call the paradox of utilitarianism -- the thought that one cannot maximize happiness if one is trying to maximize happiness. Instead, they adopt some form of indirect utilitarianism (IU), arguing that the optimal decision procedure may differ markedly from the criterion of rightness for actions. Here I distinguish between six different versions of indirect utilitarianism, arguing that the weaker versions of IU also fall prey to the paradox of utilitarianism, while the stronger versions of IU violate an overwhelmingly plausible moral principle, the principle that one ought to V only if one can V intentionally