A description of the entire configuration of liquid drops spreading over a preciously wetted solid surface is given in the case of negligible evaporation and small Bond and Weber numbers. Two solutions are developed: an outer one which is valid in the bulk of the drop and an inner solution which applies in the vicinity of the macroscopic boundary of the drop. The model accounts for deviations from the constant-curvature profile for the outer solution and, in addition, for deviations of the inner solution from the asymptotic approximation of V. V. Kalinin and V. M. Starov (1986, Colloid J. USSR (English tr.) 48, 907). Both solutions are shown to present an inflexion point. Its location is shown to be very sensitive to one parameter which fully determines the inner solution. The value of this parameter, and the spreading laws for the drop radius, the apex height, and the dynamic contact angle are determined by matching the inner and outer solutions. Results show deviations from the power laws used in the literature. These deviations are discussed in relation to the results obtained by V. M. Starov ef al. (1994, Adv. Colloid Interface Sci. 50, 187), and R. Chebbi and M. S. Selim (1997, J. Colloid Interface Sci. 195, 66), compared with the experimental data presented by V. M. Starov et al. for spreading over dry smooth solid surfaces. Moreover, the present analysis allows description of the entire drop configuration and slope and curvature variations.