The influence of pressure on the dielectric properties and phase behavior was investigated for two substituted single crystals of SrTiO3: (a)18O exchanged SrTi18O3[STO‐18] and (b) lightly doped Sr1−xCaxTiO3with x = 0.007 [SCT (0.007)]. The18O atoms in STO‐18 reduce both the quantum fluctuations of the TiO6octahedra and the frequency of the soft phonon mode, leading to a ferroelectric (FE) state via a first‐order transition with Tc∼ 24 K at 1 bar. Tcdecreases very rapidly under pressure with an initial slope of ∼ 20 K/kbar, reaching the quantum displacive limit (Tc= 0 K) near 0.7 kbar. In the case of SCT (0.007), fluctuating polar nanodomains surround the off‐center Ca dopants and grow in size as the correlation length for dipolar interactions in the SrTiO3host increases with decreasing temperature. Ultimately, the fluctuations slow down and the nanodomains “freeze” into a relaxor state with Tmax∼ 18 K; pressure reduces Tmaxwith an initial slope of ∼ 35 K/kbar. Both the FE transition in STO‐18 and the relaxor state of SCT (0.007) are completely suppressed below 1 kbar and a quantum paraelectric state emerges. © 2003 American Institute of Physics