In 2003, Waters, Felten and Sahai introduced a novel cryptographic primitive called Incomparable Public Key cryptosystem to protect anonymity of message receivers in an untrusted network. In this setting, a receiver is allowed to create many anonymous identities for himself without divulging the fact that all these identities refer to the same receiver. Recently, Lee and Lim improved the solution of Waters et al. with a more efficient decryption process. Both of these schemes are based on the ELGamal encryption scheme and are CCA1-secure in the sense of data privacy and IK-CPA-secure in the sense of key privacy. In this paper, we employ the Cramer-Shoup encryption scheme to propose the first example of an incomparable public key encryption scheme which is CCA2-secure in data privacy and IK-CCA-secure in key privacy. Therefore, our scheme outperforms existing incomparable public key schemes in security properties.