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A micromagnetic study on the magnetization reversal in bit patterned media (BPM) with each bit consisting of an exchange coupled composite (ECC) layer stack is presented. The simulations reveal superior magnetic properties of the combined ECC/BPM scheme, in particular for graded media, using uncorrelated distributions of magnetic anisotropy values in order to lower the switching field while keeping a high thermal stability of the media. In this study, a route for narrowing the switching field distribution of the bit array is provided as well, which is vital for the applicability of the BPM concept in magnetic data storage.