Detection of non-Maxwellian electron energy distribution functions (EEDFs) by Langmuir probes in the presence of radiofrequency (RF) fluctuations in the plasma potential is possible if the probe is properly RF compensated. If the non-thermal electrons are created by wave acceleration, however, they usually are bunched at one phase of the RF. In this case, the usual method of forcing the probe to follow fluctuations in the floating potential will be inappropriate, since itself will be time-dependent in such a way as to ensure that the fast electron tail is not detected. The probe must be made to follow fluctuations in the space potential. Computations are given to show the effect of a RF on distributions with high-energy tails with and without the proper compensation. Singular EEDFs arising in the case of constant energy gain are also treated for the first time.