It is often remarked that pure random noise cannot, or should not, be used for estimating frequency response on lightly damped structures. The reason given is that the bias errors caused by leakage would “deform” the estimated FRF in an unsuitable way for modal parameter processing. In this paper, traditional coherence-based methods are compared with the recently proposed local polynomium method. It is demonstrated that the bias error can be made arbitrarily small but that it requires rather long FFT blocksize, relative to what is needed with other excitation signals, such as burst random or periodic excitation signals. A main conclusion is that, while pure random is an inferior excitation signal for synthetic excitation, in cases where there is no choice, such as wind or traffic loaded structures, low-bias FRFs can very well be estimated, provided the measurement time can be long enough.