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We introduce a new dictionary structure for sparse representations better adapted to pursuit algorithms used in practical scenarios. The new structure, which we call an Iteration-Tuned Dictionary (ITD), consists of a set of dictionaries each associated to a single iteration index of a pursuit algorithm. In this work we first adapt pursuit decompositions to the case of ITD structures and then introduce a training algorithm used to construct ITDs. The training algorithm consists of applying a K-means to the (i -1)-th residuals of the training set to thus produce the i-th dictionary of the ITD structure. In the results section we compare our algorithm against the state-of-the-art dictionary training scheme and show that our method produces sparse representations yielding better signal approximations for the same sparsity level.