This paper presents a first example of secure identity based encryption scheme (IBE) without redundancy in the sense of Phan and Pointcheval. This modification of the Boneh-Franklin IBE is an hybrid construction that is proved to be secure (using proof techniques borrowed from those for KEM-DEM constructions) in the random oracle model under a slightly stronger assumption than the original IBE and turns out to be more efficient at decryption than the latter. A second contribution of this work is to show how to shorten ciphertexts in a recently proposed multiple-recipient IBE scheme. Our modification of the latter scheme spares about 1180 bits from a bandwidth point of view as, somewhat surprisingly, redundancies are not needed although all elements of the ciphertext space are not reachable by the encryption mapping. This shows that in public key encryption schemes, redundancies may be useless even when the encryption mapping is not a surjection.