Spreading of a liquid over a dry smooth solid surface is analyzed in the case of complete wetting, negligible evaporation, and small Bond and Weber numbers. In the inner region, the approach of V. M. Starov et al. (Adv. Colloid Interface Sci. 50, 187 (1994)) is used and disjoining pressure effects are included. In the core region of the drop, both capillary and viscous effects are included to account for deviations from the constant-curvature profile near the inflexion point. The spreading laws for the drop radius, the apex height, and the dynamic contact angle are determined by matching the inner and outer solutions at the inflexion point. The results are compared with the model of Starov et al. (1994) and the experimental results of J. D. Chen (J. Colloid Interface Sci. 122, 60 (1988)). The model is not based on any fitting parameter.