We have investigated homogeneous nucleation of water droplets in the vapor phase. Nucleation in water vapor has been previously studied a number of times using various experimental techniques. The nucleation pulse technique used here allows accurate measurements of homogeneous nucleation rates J vs supersaturation S in the range from 10(5) to 10(9) cm-3 s-1. The advance reported here consists of the fact that the J-S curves are measured at a selectable constant temperature. We determined the nucleation rates in supersaturated water vapor mixed with various carrier gases as functions of supersaturation and temperature (217 < T/K < 259). Nucleation is found to be nondependent of the nature of the carrier gas. Data analysis was carried out in four steps. First, we observed quantitative agreement in the range of overlap with experimental results by Miller et al. [J. Chem. Phys. 78, 3204 (1983)]. Second, experimental nucleation rates were compared with the predictions of classical nucleation theory. Systematic deviations from that theory were observed as in the case of other systems (e.g., alcohols, nonane) studied previously. Third, comparison with a new version of Fisher's droplet model reveals remarkable agreement between experiment and theory. Finally, we implemented a model-independent determination of the average nucleus size directly from the slopes of the isothermal J-S curves.