Simultaneous use of data within relatively broad frequency bands is essential to discriminating between velocity and errors in the construction of viscoacoustic full-waveform inversion (QFWI) updates. Individual frequencies or narrow bands in isolation cannot provide sufficient information to resolve parameter crosstalk issues in a surface seismic acquisition geometry. At the same time, too broad a frequency band introduces significant problems in the presence of modeling errors. The risk of modeling errors arising in QFWI is high because of the range of very different geologic contributors to attenuation and dispersion and the variety of available mathematical descriptions. We perform numerical tests that suggest that by relaxing the typical requirement that the frequency dependence of the assumed intrinsic attenuation model be self-consistent across the full spectrum, significant improvement in the fidelity of the inversion results can be obtained in cases where the attenuation model assumed in the inversion differs substantially from the true subsurface behavior. We find that the size of the frequency bands used in this inversion approach is a useful hyperparameter controlling trade-off between crosstalk reduction and flexibility in coping with uncertain physics.