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) than in helium at the same pressure. It is argued that the explanation of the two observed trends is different. For case (i), it is the insufficient thermalization of the growing water clusters in helium at the lowest pressure that has a reducing effect on the nucleation rate, although a full quantitative agreement has not yet been reached. For case (ii), thermal effects being negligible, it is the pressure dependency of the surface tension, much stronger for nitrogen than for helium, that explains the trends observed, although also here a full quantitative agreement has not yet been achieved.