We analyze the modes and coupling efficiency of asymmetric optical-fiber waveguides. We treated the step index-asymmetric optical-fiber waveguide as a boundary-value problem and obtain the expressions for the modes under logical assumptions. Using these expressions, we describe the propagation constants, mode delay, and power distribution of two asymmetric optical-fiber waveguides under consideration. Based on the perturbation theory, we also present the coupling coefficients of these asymmetric optical-fiber waveguides. We show that the waveguide parameters are considerably changed in the presence of distortion, and one can tune these parameters at the desired level by choosing suitable distortions.