Previous attempts to apply the principles of hydrostatic leveling to precision geodesy have been limited by the uniformity of the fluid density attainable in field environments. This largely due to the effects of temperature variations in the fluid tube. We have overcome this difficulty by using water maintained near its maxium density at 3.98¿C inside a counterflow heat exchanger to limit the variations in density to less than 1 ppm. We have demonstrated the feasiblitiy of this method with a 14-m prototype level and have used a computer model of the system to demonstrate the theoretical performance of instruments up to 1 km long. It appears possible, for example, to construct a fluid tube 200 m long, 12.5 cm in diameter, and weighing 3.8 kg/m that would provide uniform density to <1 ppm in field environments between -40¿ and 50¿C. In our attempt to use the 14-m prototype pressure-transfer level we were unable to exploit the denisty stability that we had achieved due to inadequacies in available pressure gauges.