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The systematic evolution of the structural, vibrational, and superconducting properties of nearly optimally doped Tl2Ba2CaCu2O(8+δ) with pressure up to 30 GPa is studied by x-ray diffraction, Raman scattering, and magnetic susceptibility measurements. No phase transformation is observed in the studied pressure regime. The obtained lattice parameters and unit-cell volume continuously decrease with pressure by following the expected equation of state. The axial ratio of c/a exhibits an anomaly starting from 9 GPa. At such a pressure level, the deviation from the nonlinear variation of the phonon frequencies is detected. Both the above observations indicate the enhancement of the distortion upon compression. The superconducting transition temperature is found to exhibit a parabolic behavior with a maximum of 114 K around 7 GPa. We demonstrate that the interplay between the intrinsic pressure variables and distortion controls the superconductivity.