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In this paper, an in-depth analysis of the possibilities of mitigating the magnetic field generated from typical overhead power lines by the use of compensated passive loops is presented. Typical conductor arrangements (flat, alternate, and super-bundle) for distribution, subtransmission, and transmission levels are compared, regarding the passive loops' characteristics (arrangement, dimensions, parametric sensibility analysis) and the mitigation effectiveness in two different typical situations of interest area: at one side (unilateral) and both sides (bilateral) from the line. The passive loop configurations considered are single loop, 3-conductor 2 loops, and 4-conductor 2 loops. Practical conclusions about the more suitable solutions are included. To obtain the optimum location of passive loops, a genetic algorithm (the major aspects will be presented) has been developed.