We examined the effect of the lattice compression on the crystal structure of the Bi2Sr2CaCu2 superconductor with nearly optimally doped and overdoped composition using X-ray diffraction technique. Our studies show that at high pressures (up to 30 GPa ) the doping level does not affect the crystal structure of this superconductor. Along with this, structural anomalies in ratio appear at a pressure that corresponds to that at which T c begins to decrease. This fact indicates a close connection between the observed anomalies and superconductivity. We also studied the effect of doping and pressure on the T c (P) and on the Raman active lattice modes of the Bi2Sr2CaCu2 superconductors. We find universal suppression of the T c by the pressure starting from the critical pressure P c in the range from 9 to 16 GPa, depending on the doping level of the Bi2Sr2CaCu2 samples. Concomitantly, we observe phonon anomalies around 10 to 20 GPa, which indicate possible pressure-induced charge redistribution in BiO layers. These newly detected anomalies may be related to the changes in the electronic structure which compete with the superconductivity.