Abstract This article deals with the erratic and inconsistent phase-noise spectra often seen in low-noise oscillators, whose floor is of the order of −180 dBc/Hz or less. Such oscillators are generally measured with two-channel instruments based on averaging two simultaneous and statistically independent measures. Our new method consists of inserting a dissipative attenuator between the oscillator under test and the phase-noise analyzer. The thermal noise of the attenuator introduces a controlled amount of phase noise. We compare the phase noise floor to the theoretical expectation with different values of the attenuation in small steps. The analysis reveals a negative bias (underestimation of phase noise) due to the thermal energy of the internal power splitter at the instrument input, and an uncertainty due to crosstalk between the two channels. In not-so-rare unfortunate cases, the bias results in a negative phase-noise spectrum, which is an obvious nonsense. Similar results are observed separately in three labs with instruments from the two major brands. We provide experimental evidence, full theory and suggestions to mitigate the problem, and a first attempt to assess the uncertainty. Our multiple-attenuators method provides quantitative information about the correlation phenomena inside the instrument.