One of the key points of interest in pyrochlore materials containing bismuth derives from the dielectric properties of some such materials that are linked to the displacements of the bismuth atoms from the ideal site. This study uses high pressure to probe the variations in, and causes of, these displacements. Under compression Bi2Ti2O7 does not undergo any phase changes, but Bi2Sn2O7 undergoes a similar series of changes to those observed during heating. The trigonal beta-Bi2Sn2O7 structure is solved from high temperature powder neutron diffraction data and hence the sequence of phases observed in Bi2Sn2O7 is discussed for the first time. The variation in Bi displacements can be considered in terms of the frustration of the tetrahedral lattice that accommodates them. It can also be inferred that the main driver for Bi displacement is a deficiency in the bond valence sum of bismuth.