The nonlinear mechanical properties of the cochlea have been recognized as signatures of active amplification by critical oscillators—active dynamical systems that each operate at a Hopf bifurcation. A critical oscillator, however, evinces a maximal sensitivity that is inversely proportional to the bandwidth of its frequency tuning, resulting in a constant “gain-bandwidth” product. The cochlea does not work by this rule: the gain-bandwidth product increases with decreasing sound-pressure levels, so that sensitivity to low sound levels is high but tuning is relatively broad. The cochlea thus appears to violate a fundamental requirement for a principle of cochlear amplification based on critical oscillators. Here, we tackle this challenge by integrating tonopically distributed critical oscillators in a traveling-wave model of the cochlea. Our nonlinear model accounts for two-dimensional hydrodynamics, longitudinal coupling between oscillators and energy pumping by the oscillators into the wave. The model produces, with a single set of parameters, a family of cochlear tuning curves over a broad range of input levels. We found that the gain-bandwidth product decreased at increasing levels, while preserving, but not precisely, the generic power-law behavior of critical oscillators. Marrying the physics of critical oscillators with traveling waves can thus account for the compressive nonlinearity underlying cochlear amplification, while ensuring that the bandwidth of the tuning curves remain relatively broad and varies little with sound level.