Wide bandgap materials such as GaN with its direct bandgap structure have been developed rapidly for applications in short wavelength light emission. ZnO, II-VI oxide semiconductor, is also promising for various technological applications, especially for optoelectronic light emitting devices in the visible and ultraviolet (UV) range of the electromagnetic spectrum. Above-band-edge absorption spectra of reactively sputtered Zn- and O-rich samples exhibit free exciton (FX) and neutral acceptor bound exciton (A degrees X) features. It is shown that the residual acceptors which bind excitons with an energy of 75 meV reside about 312 meV above the valence band, according to effective mass theory. An intra-bandgap absorption feature peaking at 2.5 eV shows correlation with the characteristically narrow A-free exciton peak intensity. Relevant annealing processes are presented as a function of time and temperature dependently for both Zn- and O- rich thin films. Enhancement of the free exciton peak intensity is observed without disturbing the residual shallow acceptor profile which is necessary for at least background p-type conductivity.