Lifting schemes (LS) were found to be efficient tools for image coding purposes. Since LS-based decompositions depend on the choice of the prediction/update operators, many research efforts have been devoted to the design of adaptive structures. The most commonly used approaches optimize the prediction filters by minimizing the variance of the detail coefficients. In this article, we investigate techniques for optimizing sparsity criteria by focusing on the use of an a"" (1) criterion instead of an a"" (2) one. Since the output of a prediction filter may be used as an input for the other prediction filters, we then propose to optimize such a filter by minimizing a weighted a"" (1) criterion related to the global rate-distortion performance. More specifically, it will be shown that the optimization of the diagonal prediction filter depends on the optimization of the other prediction filters and vice-versa. Related to this fact, we propose to jointly optimize the prediction filters by using an algorithm that alternates between the optimization of the filters and the computation of the weights. Experimental results show the benefits which can be drawn from the proposed optimization of the lifting operators.