The effects of instrument noise on estimating the spectral attenuation rates of ocean waves in sea ice are explored using synthetic observations in which the true attenuation rates are known explicitly. The spectral shape of the energy added by noise, relative to the spectral shape of the true wave energy, is the critical aspect of the investigation. A negative bias in attenuation that grows in frequency is found across a range of realistic parameters. This negative bias decreases the observed attenuation rates at high frequencies, such that it can explain the rollover effect commonly reported in field studies of wave attenuation in sea ice. The published results from four field experiments are evaluated in terms of the noise bias, and a spurious rollover (or flattening) of attenuation is found in all cases. Remarkably, the wave heights are unaffected by the noise bias, because the noise bias occurs at frequencies that contain only a small fraction of the total energy.