Rates of homogeneous nucleation of ice in micrometre-sized water droplets are reported. Measurements were made using a new system in which droplets were supported on a hydrophobic substrate and their phase was monitored using optical microscopy as they were cooled at a controlled rate. Our nucleation rates are in agreement, given the quoted uncertainties, with the most recent literature data. However, the level of uncertainty in the rate of homogeneous freezing remains unacceptable given the importance of homogeneous nucleation to cloud formation in the Earth's atmosphere. We go on to use the most recent thermodynamic data for cubic ice (the metastable phase thought to nucleate from supercooled water) to estimate the interfacial energy of the cubic ice-supercooled water interface. We estimate a value of 20.8 +/- 1.2 mJ m(-2) in the temperature range 234.9-236.7 K.