We present all-electron computations of the three-dimensional (3D) Fermi su
rfaces (FS's) in Ba1-xKxBiO3 for a number of different compositions based o
n the self-consistent Korringa-Kohn-Rostoker coherent-potential-approximati
on approach for incorporating the effects of Ba/K substitution. By assuming
a simple cubic structure throughout the composition range, the evolution o
f the nesting and other features of the FS of the underlying pristine phase
is correlated with the onset of various structural transitions with K dopi
ng. A parametrized scheme for obtaining an accurate 3D map of the FS in Ba1
-xKxBiO3 for an arbitrary doping level is developed. We remark on the puzzl
ing differences between the phase diagrams of Ba1-xKxBiO3 and BaPbxBi1-xO3
by comparing aspects of their electronic structures and those of the end co
mpounds BaBiO3, KBiO3, and BaPbO3. Our theoretically predicted FS's in the
cubic phase are relevant for analyzing high resolution Compton scattering a
nd positron-annihilation experiments sensitive to the electron momentum den
sity, and are thus amenable to substantial experimental verification.