Since W. J. Morgan proposed that intraplate volcanism at some Pacific hotspots is caused by hot plumes rising from the lower mantle, geophysicists have been actively pursuing physical evidence for mantle plumes. Several seismic studies have mapped low-velocity anomalies below a number of hotspots. However, the association of low-velocity structures with plume tails has remained controversial given the debate on whether lower-mantle plumes impart observable traveltime or amplitude perturbations on seismic waves. Using high-resolution numerical simulations of plume ascent through the mantle and their effects on waveforms, we demonstrate that the delay of shear waves by plume tails at depths larger than 1000 km are immeasurably small (<0.2 s) at seismic periods commonly used in waveform analysis. Therefore, we conclude that narrow lower mantle plumes are not detectable.