We investigated experimentally and numerically the coupling mechanism in asymmetric fused fiber couplers consisting of different single-mode fibers with unequal core diameter and numerical aperture. We increased the maximum coupled power by pretapering one of the fibers achieving a nearly complete power transfer at a specific pretaper length. Experimental results are compared to numerical results obtained by using our own three-dimensional (3D) FFT-based beam propagation method (BPM) algorithm. The numerical model explains qualitatively the coupler performance and allows to gain insight into the coupling mechanism. We discuss the influence of the fiber cores on the excited super-modes of the cladding structure. A modal decomposition of the light field is carried out in order to analyze the evolution of the super-modes and to discuss the influence of pretapering on the excitation of these modes.