At Eurocrypt 2005, Boneh-Boyen-Goh presented an interesting and important construction of a constant size ciphertext HIBE. The HIBE was proven to be secure in the selective-ID model. In this paper, we present two variants of the BBG-HIBE secure in more general security models. The first variant is proved to be secure in a generalization of the selective-ID model while the second variant is proved to be secure in the full security model. Our constructions are not straightforward modifications of the BBG-HIBE. Several techniques have to be suitably combined to obtain the required proofs.