This paper presents a novel framework for the generic construction of hybrid encryption schemes which produces more efficient schemes than the ones known before. A previous framework introduced by Shoup combines a key encapsulation mechanism (KEM) and a data encryption mechanism (DEM). While it is sufficient to require both components to be secure against chosen ciphertext attacks (CCA-secure), Kurosawa and Desmedt showed a particular example of KEM that is not CCA-secure but can be securely combined with a specific type of CCA-secure DEM to obtain a more efficient, CCA-secure hybrid encryption scheme. There are also many other efficient hybrid encryption schemes in the literature that do not fit Shoup's framework. These facts serve as motivation to seek another framework. The framework we propose yields more efficient hybrid scheme, and in addition provides insightful explanation about existing schemes that do not fit into the previous framework. Moreover, it allows immediate co...