The effect of A-site incorporated Ba2+ and Bi3+ on the pressure-driven structural transformations in Pb-based perovskite-type relaxor ferroelectrics has been studied with in situ x-ray diffraction and Raman scattering of PbSc0.5Nb0.5O3, Pb0.93Ba0.07Sc0.5Nb0.5O3, and Pb0.98Bi0.02Sc0.51Nb0.49O3 in the range from ambient pressure to 9.8 GPa. The substitution of Ba2+ for Pb2+ represents the case in which A-site divalent cations with stereochemically active lone-pair electrons are replaced by isovalent cations with a larger ionic radius and no active lone pairs, leading to formation of strong local elastic fields. In contrast, substitution of Bi3+ for Pb2+ involves the replacement of divalent A-site cations with active lone-pair electrons by aliovalent cations with nearly the same ionic radius and active lone pairs so it induces local electric fields but not strong elastic fields. The two types of dopants have rather distinct effects on the changes in the atomic structure under pressure. The embedding of Ba2+ and associated elastic fields hinders the development of pressure-induced ferroic ordering and thus smears out the phase transition. The addition of Bi3+ enlarges the fraction of spatial regions with a pressure-induced ferroic distortion, resulting in a more pronounced phase transition of the average structure, i.e., the preserved lone-pair order and the absence of strong local elastic fields enhances the development of the ferroic phase at high pressure. For all compounds studied, the high-pressure structure exhibits glide-plane pseudosymmetry associated with a specific octahedral tilt configuration.