We report an x-ray diffraction study on the charge-density-wave (CDW) LaTe₃ and CeTe₃ compounds as a function of pressure. We extract the lattice constants and the CDW modulation wave vector. We observe that the intensity of the CDW satellite peaks tend to zero with increasing pressure, thus providing direct evidence for a pressure-induced quenching of the CDW phase. Our findings further support the equivalence between chemical and applied pressures in RTe₃, put forward by our previous optical investigations, but reveal some subtle differences. We offer a possible explanation for these differences.