Differences and similarities between LiF-based LiF:Mg,Ti and LiF:Mg,Cu,P are discussed, with respect to their dosimetric properties--sensitivity, non-linearity of dose response and heavy charged particle efficiency, as related to the concentration and the individual role of the Mg, Ti, Cu and P dopants. To study further the role of these dopants, the properties of some new, 'hybrid' phosphors: LiF:Mg,Cu,Ti and LiF:Mg,P, specially developed for this purpose, are also discussed. In the glow curve of LiF:Mg,Cu,P with a low concentration of Mg a new peak was found, which appears to be an analogue of peak 4 in LiF:Mg,Ti, Magnesium apparently controls most of the dosimetric properties of LiF-based phosphors. For instance, charged-particle efficiency appears to be anti-correlated with the concentration of Mg, being much less dependent on the content of other dopants. On the other hand, some properties of LiF-based systems seem to be correlated with changes in the emission spectra. It is suggested that Ti hampers the acceptance of any increased amount of Mg into more traps in LiF:MgTi. The absence of Ti, not the presence of P or Cu, is therefore a key to the high sensitivity of LiF:MgCuP.