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The design of Finite Impulse Response (FIR) filters in one or several dimensions can be performed with good computational efficiency using a Weighted Least Square (WLS) design. Minimax design, which is often preferred, is computationally burdensome, principally in two dimensions. This paper draws attention to the design of minimax filters using iterative WLS techniques for one-dimensional filters and extends the approach to two-dimensional filters. For two dimensions the techniques apply to both rectangular and hexagonal sampling grids. Examples demonstrate flexibility and good computational efficiency. The paper also illustrates a promising new approach to filter design which couples the very general WLS methodology to the less manageable but often preferred minimax performance criterion.