Responses to acoustic stimuli in the cochlea are known to be nonlinear. Many existing models of cochlear mechanics were built upon three basic assumptions: traveling-wave amplification is provided by active mechanisms in the outer hair cells (OHCs). Second, as the stimulus level increases, the gain decreases due to saturation nonlinearity in the OHCs. Finally, the saturation non-linearity is "instantaneous"; its input-output relation does not possess memory. These assumptions were recently challenged by reports that basilar-membrane (BM) responses to noise can be predicted well by level-dependent Wiener filters and are thus quasi-linear. It was argued that the quasi-linear responses could not result from instantaneous nonlinearity. In this paper, we present a model of cochlear mechanics which has instantaneous OHC saturation nonlinearity but produces quasi-linear responses to noise. Correlation coefficients were consistently greater than 0.9 between simulated noise responses and the responses predicted by equivalent Wiener filters. Further, Gaussianity in the acoustic stimuli was preserved on the BM. We conclude that the results support the common understandings and assumptions of cochlear mechanics.