Abstract The effect of hydrostatic pressure (up to 12 kbar) on the phonon and electron characteristics of lead and lead-indium alloys have been studied in detail by electron tunnelling. Quantitative data on the change of the superconducting energy gap and the Van Hove Singularities for the phonon spectra were obtained. The energy dependence of the microscopic Gruneisen parameters was found for Pb–In alloys. We present consistent data on the pressure dependence of the electron–phonon interaction characteristics, particularly the function α2(ω)F(ω), the renormalization function Z N(ω), and the electronic characteristic parameter E. The experimental tunnelling density of states is in qualitative agreement with that calculated from the Eliashberg equations. This comparison confirms the accuracy of the basic equations for superconductivity under changes of volume. An analysis of the pressure dependence of the superconducting transition temperature T c is made on the basis of the exact and approximate expressio...