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A precise theoretical investigation is made on ion-acoustic (IA) solitary waves (SWs) and double layers (DLs) in a degenerate multi-ion plasma (composed of inertial positive and negative ions and degenerate electrons). The standard reductive perturbation method is employed to derive the Korteweg-de Vries (K-dV), the mixed K-dV (mK-dV), and the Gardner (GE) equations. The GE admits SW and DL solutions for μ around its critical value μc (where μc is the value of μ corresponding to the vanishing of the nonlinear coefficient of the K-dV equation). The basic features of IA SWs and DLs are analyzed. It is found that the characteristics of IA SWs found from GE are different from those of the K-dV solitons and mK-dV solitons. The implications of our results to different space and laboratory plasma situations, where opposite polarity ions are observed, are briefly discussed.