The paper discusses Bernard Williams’ argument that immortality is rationally undesirable because it leads to insufferable boredom. We first spell out Williams’ argument in the form of a dilemma. We then show that the first horn of this dilemma, namely Williams’ requirement of the constancy of character of the immortal, is defensible. We next argue against a recent attempt that accepts the dilemma, but rejects the conclusion Williams draws from it. From these we conclude that blocking the second horn of the dilemma is the best way to respond to Williams. Our objection contends that Williams overlooks a basic feature of human existence, namely curiosity, and that his negative evaluation of an eternal life is therefore unconvincing.