Switchable atomic displacements generate electric dipole moments in ferroelectric materials utilized in many contemporary devices. Lead titanate, a perovskite oxide with formula PbTiO3, has been referred to as a textbook example of a prototype displacive ferroelectric and is a testing platform of widely used models of piezoelectric response of complex solid-solutions. PbTiO3 has been addressed by experimental and computational studies, often with apparently conflicting conclusions. To date, hydrostatic pressure experiments have been interpreted in terms of a model in which the dipole moments gradually diminish with increasing pressure until a transition to a cubic phase, characterized by a zero average dipole moment, occurs. The model unrealistically assumes an even compression of the crystal. Here we show by high-pressure neutron powder diffraction measurements that a fast and slow shrinkage of 12-oxygen cages around Pb and octahedra around Ti, respectively, takes place. A phase diagram consolidating earlier and present results is given.