We revisit the problem of constructing a protocol for performing authenticated encryption with associated data (AEAD). A technique is described which combines a collision resistant hash function with a protocol for authenticated encryption (AE). The technique is both simple and generic and does not require any additional key material beyond that of the AE protocol. Concrete instantiations are shown where a 256-bit hash function is combined with some known single-pass AE protocols employing either 128-bit or 256-bit block ciphers. This results in possible efficiency improvement in the processing of the header.