E-mail brings us lots of conveniences. Especially with help of PGP and S/MIME, it gives both confidentiality and message/origin authentication. However, in some cases for strong privacy, a message sender will not want to let others know even the fact that he sent a message to a recipient. Very recently, Harn and Ren proposed a fully deniable authentication scheme for E-mail where a sender can repudiate his or her signature. In this paper, however, their deniable authentication scheme is proved not to be fully deniable. To resolve this deniability problem, we suggest a designated verifier signature scheme to support strong privacy, and construct a privacy-enhanced deniable authentication E-mail scheme using the designated verifier signature scheme. Compared with the Harn and Ren's scheme, the proposed scheme has a simple cryptographic structure and can be easily realized with the existing secure E-mail systems.