We examine the problem of approximating a complex frequency response by a real-valued FIR filter according to the L₂ norm subject to additional inequality constraints for the complex error function. Starting with the Kuhn-Tucker optimality conditions which specialize to a system of nonlinear equations we deduce an iterative algorithm. These equations are solved by Newton's method in every iteration step. The algorithm allows arbitrary tradeoffs between an L₂ and an L_oo design. The L₂ and the L_oo solution result as special cases.