Many seismic attenuation measurements, and particularly those using local earthquakes and seismic codas, result in large exponents h ≥ 1 in the frequency-dependent quality factor Q(f) = Q0fh. However, such steep positive frequency dependences of Q are highly problematic physically. Specifically, the case of h = 1 corresponds to frequency-independent (elastic) amplitude decays with time and consequently requires no Q-type attenuation mechanisms. In this case, parameter Q0 actually describes the frequency-independent amplitude decay in access of some assumed geometric spreading t-a, where it is usually (often inaccurately) assumed a = 1. For h > 1, there are three problems with physical meanings of such Q-factors. First, contrary to the key premise of seismic attenuation, high-frequency parts of the wavefield are enhanced with increasing propagation times relative to the low-frequency ones. Second, such attenuation cannot be implemented by mechanical models of wave-propagating media. Third, the velocity dispersion associated with such Q(f) occurs over unrealistically short frequency range and has an unexpected oscillatory shape. Cases h = 1 and h > 1 are usually attributed to scattering; however, this scattering must exhibit fortuitous tuning into the observation frequency band, which is unlikely. Thus, the case h > 1 is not allowed physically and could serve as an indicator of problematic interpretations. Although case 0 < h < 1 is possible, its parameters Q0 and h may also be biased by the measurement procedure. The reason for these problems is that the inferred Q values are affected by the conventional parameterization of attenuation by a Q factor. Both parameters Q0 and h are apparent, i.e. dependent on the selected parameterization and inversion method, and they should not be directly attributed to the subsurface. To avoid the uncertainties of Q, we recommend measuring and interpreting the amplitude-decay rates directly, such as by using parameter a above.