Single-wall carbon nanotubes (SWNTs) under in-situ pressures of 0-0.5 GPa have been studied using Raman scattering in a diamond anvil cell (DAC). The pressure-induced changes in electronic structure of SWNT were related to changes observed in resonant Raman spectra. In particular, the radial breathing Raman modes show a strong pressure dependence. At ambient conditions the band at 191 cm-1, corresponding to SWNTs with a diameter of 1.29 nm was a dominant spectral feature, whereas at pressures above 0.3 GPa, the band at 211 cm-1, corresponding to nanotubes with a smaller diameter (1.16 nm), became dominant. The switching of resonance enhancement in selective diameter SWNTs is interpreted as a pressure-induced narrowing of the corresponding electronic gap. Upon decompression these effects are reversed. Our estimation of the band gap narrowing with pressure is in agreement with the direct measurement from optical absorption experiments on SWNT surfactant liquid suspension pressurized in a DAC.