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Under some circumstances, the power flux density produced by emissions from a spacecraft suffers the presence of spurious frequencies. This occurs, for example, when idle data with long sequences of zeros are transmitted. At high data rates, randomizers may not be able to solve the problem. Because of the need to comply with the recommendations and standards, this can reflect on severe limits on the maximum data rates achievable. Such problem, experimentally observed in some recent missions, was first studied by Alvarez and Lesthievent, but an effective solution has not been found yet. We discuss the topic and formulate three proposals to compensate the drawback. We show they permit to reduce significantly the required margin at high data rates.