Recently it has been shown that CdTe has two transitions over a narrow pressure range at ∼3.5 GPa: first zinc-blende to cinnabar and then cinnabar to NaCl. In the present work we report on the measurements of the optical absorption edge of the: (i) zinc-blende CdTeI (E g gap, Γ 1 5 v → Γ 1 c ) phase in both increasing and decreasing hydrostatic pressure up to 5 GPa using methanol-ethanol as the pressure transmitting medium; (ii) rocksalt CdTeIII phase using a new type of infrared diamond anvil cell from 6 to 10 GPa with argon as the pressure medium. From the analysis of the data it has been established that: (a) the E g gap exhibits a sublinear increase with pressure with the corresponding linear gap deformation potential being -3.8 eV; (b) absence of any discontinuity in the direct energy gap in the pressure range 3.5-4.2 GPa suggests that the gap of the reported CdTeII (cinnabar) phase is similar to that of the zinc-blende phase; and (iii) the rocksalt CdTeIII phase is not metallic but shows a broad absorption edge with onset near 0.08 eV at 6.8 GPa. The blue shift of this energy is about 1.7 10 - 2 eV GPa - 1 .