The basilar membrane in the cochlea can be modeled as an array of fluid coupled segments driven by stapes vibration and by the undamping nonlinear force simulating cochlear amplification. If stimulated with two tones, the model generates additional tones due to nonlinear distortion. These distortion products (DPs) can be transmitted into the ear canal and produce distortion-product otoacoustic emissions (DPOAEs) known to be generated in the healthy ear of various vertebrates. This study presents a solution for DPs in a two-dimensional nonlinear cochlear model with cochlear roughness-small irregularities in the impedance along the basilar membrane, which may produce additional DPs due to coherent reflection. The solution allows for decomposition of various sources of DPs in the model. In addition to the already described nonlinear-distortion and coherent-reflection mechanisms of DP generation, this study identifies a long-latency DPOAE component due to perturbation of nonlinear force. DP wavelets that are coherently reflected due to impedance irregularities travel toward the stapes across the primary generation region of DPs and there evoke perturbation of the nonlinear undamping force. The ensuing DP wavelets have opposite phase to the wavelets arising from coherent reflection, which results in partial cancellation of the coherent-reflection DP wavelets.