The deviation functions for thermocouples, representing the difference between thermocouple emf and the corresponding reference function, are examined using data on 367 thermocouples of types R and S, submitted for calibration over the period 1984 to 1996. Calibrations were conducted with the CSIRO National Measurement Laboratory (NML) calibration facility, which thermoelectrically scans the wires, automatically collects comparison data to 1100 °C and incorporates data from the melting point of palladium. It is shown that deviation functions are well behaved, changing gradually with temperature, and that relatively accurate calibrations may be carried out with few calibration temperatures. For example, a calibration to ~1064 °C may rely on two fixed points, those of aluminium and gold, and a calibration to 1550 °C on three fixed points, those of Al, Au and Pd. Such an approach is feasible for Pt-based thermocouples because linear interpolation over temperature intervals of ~500 °C contributes no more than about 3 µV to the expanded uncertainty of calibration.