Abstract. We build on the new security notion for deterministic encryption (PRIV) and the PRIV-secure schemes presented by Bellare et al at Crypto'07. Our work introduces: 1) A generic and efficient construction of deterministic length-preserving hybrid encryption, which is an improvement on the scheme sketched in the above paper; to our best knowledge, this is the first example of length-preserving hybrid encryption; 2) postquantum deterministic encryption (using the IND-CPA variant of code-based McEliece PKE) which enjoys a simplified construction, where the public key is re-used as a hash function. Key words: deterministic encryption, hybrid encryption, code-based encryption, searchable encryption, database security