Coordinate-measuring machines (CMMs) are widely used to measure the characteristics of various geometrical features. The measurement results using CMMs include systematic errors. To eliminate the systematic errors, the multiple-orientation technique is effective for rotationally symmetric workpieces such as cylinders or gears. However, there are Fourier components of the calibration curve that cannot be analyzed on the basis of the number of orientations; therefore, the number of orientations was set to be larger than the number of required Fourier components. Such a method takes, however, a very long time and it is difficult to maintain a stable environment during the measurement. In this paper, we propose a new measurement strategy for reducing the total number of orientations by compensating the deficient Fourier components using the measurement result with another number of orientations. When the lowest common multiple of integers m and n is set to be larger than the number of required Fourier components, the calibration result can be obtained from m + n - 1 orientations. To select m and n most efficiently, the combination should not include a common prime number. The effectiveness of the combination measurement strategy for the multiple-orientation technique was demonstrated by calibrating a multiball artifact and a gear.