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This paper presents a novel framework for generic construction of hybrid encryption schemes secure against chosen ciphertext attack. Our new framework yields new and more efficient CCA-secure schemes, and provides insightful explanations about existing schemes that do not fit into the previous frameworks. This could result in finding future improvements. Moreover, it allows immediate conversion from a class of threshold public-key encryption to a hybrid one without considerable overhead, which is not possible in the previous approaches. Finally we present an improved security proof of the Kurosawa-Desmedt scheme, which removes the original need for information-theoretic key derivation and message authentication functions. We show that the scheme can be instantiated with any computationally secure such functions, thus extending the applicability of their paradigm, and improving its efficiency.