  We study the effects of pressure on the electron-phonon interaction in MgB_2
using density-functional-based methods. Our results show that the
superconductivity in MgB_2 vanishes by 100 GPa, and then reappears at higher
pressures. In particular, we find a superconducting transition temperature T_c
\~ 2 K for mu*=0.1 at a pressure of 137 GPa.
