This paper shows how de Finetti's book-making principle, commonly used to justify additive subjective probabilities, can be modi-ed to agree with some nonexpected utility models.More precisely, a new foundation of the rank-dependent models is presented that is based on a comonotonic extension of the book-making principle.The extension excludes book-making only if all gambles considered induce a same rank-ordering of the states of nature through favorableness of their associated outcomes, and allows for nonadditive probabilities.Typical features of rank-dependence, hedging, ambiguity aversion, and pessimism and optimism, can be accommodated.