We report on the use of an active Langmuir probe with three-harmonic compensation to diagnose rf discharge plasmas driven at 13.56 MHz. The plasma generates many harmonics on the fundamental, the first few being strongest. This gives a multi-harmonic rf voltage across the probe sheath that is removed by applying a rf signal to the probe that is matched both in amplitude and in phase for each harmonic. The probe I-V characteristic can then be analysed using dc theory. We show here that only when the rf harmonic amplitude approaches about 2T_e is it necessary to compensate for that harmonic. For the commercial processing rig used this only occurs for the second harmonic at low pressures, < 5×10^-3 mbar. Here the addition of second-harmonic compensation shifts the probe I-V curve, making it markedly more positive than for fundamental-only compensation. Despite this the values obtained for the electron density n_e and temperature T_e changed by less than 10%. For most plasmas in which the harmonics have amplitudes below T_e the use of fundamental-only compensation is adequate for all but the most precise measurements.