By analysing the results of a previous experimental work it has been found that the transition changes from a liquid-gas type at low pressure to a liquid-liquid one at high pressure. However, not much experimental data are available in the literature at high Xe concentrations, and some criticism can be applied to them. Therefore, new measurements of the isobaric coexistence curves for He-Xe mixtures at three pressures (80, 132, 200 atm) have been performed, with the use of a more precise technique, based on energy resolved neutron transmission measurements. A qualitative agreement with the previous data has been found, while a disagreement is present in the behaviour ofTcversuspc, thus confirming our picture of a change in the nature of the transition as the pressure increases.