Low coverage water adsorption on the alpha-Al2O3(0001) surface has been studied with a generalized-gradient density functional approach using embedded cluster and periodic slab methodologies. An advanced cluster embedding method in an elastic polarizable environment (EPE), which enables an accurate description of the adsorption-induced substrate relaxation, has been applied systematically at various density functional levels: PW91, BP, and PBEN. In addition, periodic slab model calculations based on the PW91 functional were carried out for varying surface supercell sizes, ( 2 x 2) and ( 3 x 3), which compare very well with the corresponding embedded-cluster results. In agreement with two recent studies employing integrated MO + MO (IMOMO) embedded cluster and periodic Car - Parrinello BLYP methodologies, our calculations predict the 1,2-dissociative adsorption to be about 10 kcal mol(-1) more favorable than molecular adsorption; however, at variance with the latter study, we predict 1,4-dissociative adsorption to be least favorable. Analysis of adsorbate-induced relaxation renders the interaction energy with the unrelaxed substrate in the 1,4-dissociative case negative (unbound complex), thus rationalizing the smallest ( by absolute value) interaction energy. Our best estimates for binding energies, at the PBEN level, for molecular, 1,2-dissociative, and 1,4-dissociative adsorption are -22.5, -31.2, and -17.2 kcal mol(-1), respectively.