It is widely accepted, that nonlinear elastodynamic methods are superior to linear methods in detecting early stages of material deterioration. A number of recently developed methods are reported to be particularly sensitive to nonlinearities and thus appropriate to indicate early damage. We applied systematically one of the methods, the sideband peak count index (SPC-I), to a series of increasingly damaged carbon fiber reinforced plastic (CFRP) plates. Our data leads to different conclusions. The SPC-I values are influenced by (usually undocumented) variations in the index calculation procedure, which is not acceptable for a robust method. Moreover, the behavior of the index when the ultrasound amplitude is varied contradicts material nonlinearity as a direct and significant contributor to the index value. To clarify the apparent contradiction of our results with the previously published statements, it is recommended that (a) our data are re-evaluated by independent researchers and (b) the experiments already published are repeated or (if sufficient data is available) also re-evaluated.