Recommendations by NCRP and ICRP for a selective increase of the quality factor for neutrons have not been implemented in the practice of radiation protection, but have added urgency to the search for a more consistent new convention on quality factors. In response to this need, a liaison group of ICRP and ICRU has proposed numerical changes, but also a replacement of the reference parameter LET by the microdosimetric variable lineal energy. This would make quality factors and dose equivalents measurable, but would make computations more complicated. To resolve the dilemma, it is proposed to use an equivalence relation between lineal energy and LET which leads to nearly identical definitions whenever one deals with charged particles of sufficiently long range, For photons below 200 keV and for neutrons below 0.5 MeV, the equivalence is imperfect, but it may, even in these cases, be acceptable for the practical purposes of radiation protection.