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An extension of blind source extraction (BSE) of one or a group of sources to the case of ill-conditioned and post-nonlinear (PNL) mixing is introduced. This is achieved by a ldquomixed objectiverdquo type of cost function which jointly maximizes the kurtosis of a recovered source and estimates a measure of nonlinearity within the mixing system. This helps to circumvent problems with existing BSE methods, which are limited to noiseless and linear mixing models. Simulations illustrate the performance of the proposed algorithm and its usefulness, especially in the presence of very ill-conditioned mixing systems.