This paper presents a new analysis of C.G. Hempel's conditions of adequacy for any relation of confirmation (Hempel 1945), differing from the one Carnap gave in §87 of his (1962). Hempel, it is argued, felt the need for two concepts of confirmation: one aiming at true hypotheses and another aiming at informative hypotheses. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative hypotheses. I then show that one can have Hempel's cake and eat it too. There is a logic that takes into account both of these two conflicting aspects. According to this logic, a sentence H is an acceptable hypothesis for evidence E if and only if H is both sufficiently plausible given E and sufficiently informative about E. Finally, the logic sheds new light on Carnap's analysis.
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