A small closed-cycle liquefier and cryostat, liquefying He3 by Joule-Thomson expansion, is described. Its characteristics, operation, and performance are discussed. The JT expansion takes place from pressures of 4 atm abs or less at flow rates up to 14 litres (s t p) min−1. The closed cycle character of the circulation is maintained by use of an oil-free diaphragm compressor. The coefficient of liquefaction at an input pressure of 4 atm is about 59%, which at the maximum flow of 14 litres (s t p)−1 corresponds to a refrigerative capacity at 3·2 K of 230 mW. When used as a cryostat, the liquid He3 chamber has a capacity of 40 cm3 and this can be filled in a few minutes. Using a built-in adsorption pump, temperatures down to 0·25 K can be maintained for periods up to 50 hours under conditions of minimal refrigerative loading. Using the quantitative results obtained with this liquefier, deductions are made regarding the inversion curve of He3 and a design has been made for a cryostat covering the temperature range 0·25 K and upwards, which does not require any liquid refrigerants, such as liquid nitrogen, liquid hydrogen, or liquid helium.