Glycidyl azide-r-(3,3-bis(azidomethyl)oxetane) copolymers were synthesized by cationic copolymerization of epichlorohydrin and 3,3-bis(bromomethyl)oxetane, using butane-1,4-diol as an initiator and boron trifluoride etherate as a catalyst, followed by azidation of the halogenated copolymer. The main objective of this work is the preparation of an OH-terminated amorphous polymer with energetic content higher than that of the well-known glycidyl azide homopolymer. The effect of experimental conditions, i.e., the rate of monomer feeding, on the final molecular weight and functionality of the copolymer has also been investigated. The obtained copolymers were extensively characterized to determine their composition and thermal stability. The heat of reaction for the polymerization of the halogenated key precursors has also been measured. It was found that even though both the operating conditions and the catalytic system were chosen in order to favor a living character of the polymerization, the final product seems to be the result of a combined living and active chain end mechanism. In particular, the latter is responsible for the formation of oligomers and not hydroxyl-terminated chains. Nevertheless, the average number of OH groups is high enough to allow a cross-linking of the polymeric chains, by addition of polyisocyanates and subsequent formation of inter-chain urethanic bonds.