  The phonon dispersion and the electron-phonon interaction for the $\beta$-Po
and the bcc high pressure phases of tellurium are computed with
density-functional perturbation theory. Our calculations reproduce and explain
the experimentally observed pressure dependence of the superconducting critical
temperature (T$_{\rm c}$) and confirm the connection between the jump in
T$_{\rm c}$ and the structural phase transition. The phonon contribution to the
free energy is shown to be responsible for the difference in the structural
transition pressure observed in low and room temperature experiments.
