The distortion of the Fermi surfaces of the noble metals as a result of hydrostatic pressure has been studied by the observation of phase changes in de Haas-van Alphen oscillations in the pressure range 1 to 25 atm at 1 $^\circ$K. A relative change of phase with pressure between  belly and neck oscillations has been observed: the direction of the change shows that the neck cross-sections are increasing in size relative to the bellies. Measurements by a null method of the absolute phase change with pressure of the belly oscillations in a steady magnetic field have also been made. Despite complications due to intermodulation effects from the neck oscillations, these measurements have shown that the rates of increase of the belly cross-sections are somewhat smaller than would be expected from published figures for compressibility. A combination of these results with the measurements of relative phase change show that the overall rates of increase with pressure for the neck cross-sections are in copper about 4.2, in silver about 7.3 and in gold about 5.4 times greater than would be the case if the Fermi surface simply expanded uniformly with the Brillouin zone.