Different methods were employed to synthesize a series of high quality PbMo6S8 Chevrel-phase compounds. All the samples were characterized by means of X-ray diffraction, Auger electron spectroscopy, specific heat, acsusceptibility, resistivity, scanning electron spectroscopy and microprobe analysis. A marked decrease in the superconducting transition temperature (T(c)) and the hexagonal lattice constant ratio (c/a) were noticed on the samples prepared in quartz tubes. Based on a simple correlation between T(c) and c/a ratio, we present some of the significant structure-property relations and phase purity of the samples. This interdependence is discussed mainly in terms of oxygen content in the phase. For instance, oxygen-free samples have T(c) invariably above 14.5 K. Interestingly, the optimal T(c) is found in samples having rather different, from each other, crystallographic parameters, but with a same c/a ratio. On the other hand, the wide variation of T(c) and structural parameters of PbMo6S8 observed in the present investigation and those of many earlier works are explained by the presence of varying amounts of oxygen in the ternary phase. These results are checked in parallel with the oxygen-doped (PbMo6S8-xOx; x greater-than-or-equal-to 0.2) samples.