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In this paper we investigate for the first time the applicability of the concepts and algorithms of Multiple Criterion Optimization to the problem of optimally trading-off magnitude and phase in IIR digital filters design. Particular attention is paid to the mathematical formulation of the simultaneous magnitude and phase design problem. Three different design criteria are introduced. The special modifications of a standard algorithm  necessary for filter design are discussed. Examples of what can be expected from magnitude-phase trade-offs are discussed. The results of this work is expected to be practical CAD tools for designing simultaneous magnitude and phase optimal filters and theoretical information about the optimal trade-offs between magnitude and phase.