The paper is concerned with the question of the existence of moral dilemmas, conceived of as situations involving a subject in a conflict of non-overridden moral obligations. I reject some of the presuppositions underlying discussions of this question and argue that certain morally relevant choices cannot be evaluated in relation to an all-things-considered moral obligation as permissible or impermissible, right or wrong. In arguing for the inadequacy of our ordinary moral predicates for fully capturing the nature of such choices, I argue that they are, in certain respects, inexpressible.