Broadband transient sounds, such as clicks, are transduced in a traveling wave in the cochlea that spreads from base to apex. This traveling wave causes delays in the activation of auditory nerve fibers that vary systematically as a function of the tonotopy in the ventral cochlear nucleus (VCN) in the brainstem, activating high-frequency fibers first. Octopus cells in the mammalian VCN consistently spread their dendrites across the tonotopic axis so that the tips receive input from fibers tuned to the highest frequencies. As a result, broadband transient sounds produce a somatopetal (soma-directed) sweep of activation in octopus cells’ dendrites. Low-voltage-activated potassium channels (gKL) in the dendrites and soma sharpen the sensitivity to sweep duration. Branch points in octopus cells’ dendrites show significant impedance mismatch, resulting in violation of Rall’s “3/2 power law” and shaping of sweep sensitivity. Thus, the morphology, connectivity, and membrane biophysics of octopus cells allow them to compensate for the cochlear traveling wave delay and respond to clicks with exquisite temporal precision. In the context of the time–frequency (Gabor) uncertainty principle, octopus cells can be seen to solve a general problem of encoding frequency-dispersed but temporally restricted patterns using somatopetal sweep sensitivity. Compensation for longer delays in low-frequency hearing animals, implications for downstream processing, and relationship to other systems are discussed.