Perturbation signals for linear system identification in the frequency domain are considered. The fundamental requirement is for a low-amplitude signal with as much power as possible contained in specified harmonics. For the purposes of comparison, two new measures of signal quality are developed. The first relates the power contained in the specified harmonics to the amplitude of the signal. The second relates the least power of any specified harmonic to the average power of the specified harmonics, It is seen that perturbation signal design is a compromise between these two measures. Two classes of signal are examined, each containing several different signal types. In the first class are computer-optimised signals, with power spectra that meet a harmonic specification as closely as possible. In the second class are pseudo-random signals, with fixed power spectra. The qualities of the signals in meeting four harmonic specifications are compared, giving three overall conclusions. First, the new measures of signal quality provide an excellent basis for comparing perturbation signals. Secondly, signals with only odd harmonics present are to be preferred to signals with all harmonics present. Thirdly, it is very useful to have available the different types of computer-optimised perturbation signals, and that pseudo-random signals provide highly acceptable alternatives when the specification is for uniform power in specified harmonics.