When we hear, sound-induced deflections of our sensory outer-hair-cell bundles are transduced into receptor currents. These receptor currents drive the cochlear amplifier, which is required for our ear's high sensitivity, broad dynamic range, and sharp frequency selectivity. Adaptation maintains the sensitivity of receptor currents to bundle deflections, but the mechanisms underlying adaptation in outer-hair-cell bundles remain under debate, and how adaptation works at physiologically relevant frequencies is unclear. We propose a mechanism for the fastest components of adaptation, based on viscoelastic adaptation elements. To evaluate this proposal, we fit a mathematical model of an outer-hair-cell bundle with viscoelastic adaptation elements to twelve independent experimental observations. We validate the model by successfully predicting an observation not used for fitting --- how much receptor-current sensitivity is maintained by fast adaptation. The experimentally constrained model predicts the effects of fast adaptation for physiologically relevant frequencies. We show that there is considerable deflection-current hysteresis, the receptor current can lead the bundle deflection to a large extent (up to 61° phase lead), and that fast adaptation greatly high-pass filters the receptor current. Owing to viscoelastic fast adaptation, the dynamic range of the outer-hair-cell bundle depends on the stimulus frequency. These predictions and others are experimentally testable. Because viscoelastic fast adaptation substantially affects receptor-current sensitivity, hysteresis, phase leads, high-pass filtering, and dynamic range, we expect viscoelastic fast adaptation to greatly impact the cochlear amplifier and hearing. Here, we provide the experimental data used to constrain the mathematical models and the modeling code.