The results are presented of three-dimensional model studies of the photodissociation of the water dimer following excitation in the first absorption band. Diabatic potential-energy surfaces are used to investigate the photodissociation following excitation of the hydrogen bond donor molecule and of the hydrogen bond acceptor molecule. In both cases, the degrees of freedom considered are the two OH-stretch modes of the molecule being excited, and the dimer stretch vibration. The diabatic potentials are based on adiabatic potential surfaces computed with the multireference configuration-interaction method, and the dynamics of dissociation was studied using the time-dependent wave-packet method. The dynamics calculations yield a donor spectrum extending over roughly the same range of frequencies as the spectrum of the water monomer computed at the same level of theory. The acceptor spectrum has the same width as the monomer spectrum, but is shifted to the blue by 0.4-0.5 eV. The dimer spectrum obtained by averaging the donor and the acceptor spectrum is broader than the monomer spectrum, with the center of the dimer first absorption band shifted to the blue by about 0.2 eV relative to the monomer band. Our reduced dimensionality calculations do not find the red tail predicted for the dimer first absorption band by Harvey et al. [J. Chem. Phys. 109, 8747 (1998)]. This conclusion also holds if preexcitation of the dimer stretch vibration with one or two quanta is considered.