We here report a detailed high-pressure infrared transmission study of BiTeCl and BiTeBr. We follow the evolution of two band transitions: the optical excitation beta between two Rashba-split conduction bands, and the absorption. across the band gap. In the low-pressure range, p < 4 GPa, for both compounds beta is approximately constant with pressure and. decreases, in agreement with band structure calculations. In BiTeCl, a clear pressure-induced phase transition at 6 GPa leads to a different ground state. For BiTeBr, the pressure evolution is more subtle, and we discuss the possibility of closing and reopening of the band gap. Our data is consistent with a potential Weyl phase in BiTeBr at 5-6 GPa, followed by the onset of a structural phase transition above 7 GPa.