Maximizing Hedonism maintains that the most pleasurable pleasures are the best. Francis Bradley argues that this is either incompatible with Mill’s Qualitative Hedonism, or renders the latter redundant. Some ‘sympathetic’ interpreters respond that Mill was either a Non-Maximizing Hedonist or a Non-Hedonist. However, Bradley’s argument is fallacious, and these ‘sympathetic’ interpretations cannot provide adequate accounts of: Mill’s identification with the Protagorean Socrates; his criticisms of the Gorgian Socrates; or his apparent belief that Callicles is misguided to attempt to show that the pleasures of the intelligent can be more valuable than the pleasures of fools without also being more pleasurable.