Recent philosophical writing on sexual desire divides broadly into two camps. Reductionists take sexual desire to aim at an essentially physical bodily pleasure, whereas intentionalist accounts take a focus upon the reciprocal interaction of the mental states of the partners to be crucial for understanding the phenomenon. I argue that the apparent plausibility of reductionism rests upon the flawed assumption that sexual pleasure has the same uniform bodily character in all sexual encounters, which rests in turn upon flawed assumptions in the philosophy of mind. Drawing on an Aristotelian understanding of persons as essentially embodied minds, I outline an alternative account of sexual desire, showing how the nature of the sexual pleasure we take in the body of another can be transformed by the significance the person or situation has for us. I proceed to show that my account of sexual desire is able to accommodate the entire range of sexual phenomena, including those that seem to undermine standard intentionalist accounts as well as those that reductionists have difficulty in fully explaining. Finally I make some brief remarks about the implications of my account of sexual desire for sexual morality, suggesting some reasons why it casts doubt on the view that universal participant consent is sufficient for a sexual act to be morally unproblematic.