Homogeneous nucleation rates of water droplets were measured at a nucleation temperature close to 240 K in a Pulse-Expansion Wave Tube (PEWT). Several measures were taken to improve the data obtained with the PEWT. For instance, the molar water vapor fraction was determined with three independent techniques. The resulting standard uncertainty of the supersaturation was within 1.8%. Results are given for water nucleation in helium at 100 kPa and at 1000 kPa and in nitrogen at 1000 kPa. Two trends were observed: (i) the values of the nucleation rate of water in helium at 1000 kPa are slightly but significantly higher (factor 3) than its values at 100 kPa and (ii) nucleation rates of water in nitrogen at 1000 kPa are clearly higher (factor 10)...