A study specifically intended to measure the triple-point temperature of both n-D₂ and e-D₂ containing a volume fraction of HD not higher than 0.0001 has been completed. It was performed by measuring samples of gas in metal sealed cells. The cells, after being checked for a non-increasing HD contamination within the stated limits, were filled by directly connecting them to the outlet of a thermal-diffusion column for isotopic separation, known to produce D₂ with a HD volume fraction not larger than 0.00003. In the case of e-D₂, additional studies were performed on the effect of deuterating the catalyst or on high-temperature activation of the catalyst. Results proved that it is possible to obtain good results for e-D₂ with partially deuterated catalyst, but this does not allow a reliable control of the contamination. An alternative procedure to full deuteration has been found, which uses commercial hydrous ferric oxide heated to about 400 °C, and commercially available deuterium, produced by isotopic separation and showing a purity better than 99.99%. Temperature values (18.7327 ± 0.0003) K for n-D₂ and (18.6983 ± 0.0003) K for e-D₂ on NPL-IPTS-68 were obtained at the liquidus point; the best thermodynamic values for these triple points are (18.723₂ ± 0.001) K and (18.688₈ ± 0.001) K respectively; e-D₂ can be used as a first-quality temperature reference point.