A simple model is presented to describe the nonmetallic behavior obser
ved over wide doping ranges of perovskite-type BaBi1-xPbxO3 and Ba1-xK
xBiO3 alloys. The model is based on the idea that the oxygen octahedra
endure static distortion waves of a ''breathing'' type, with wave vec
tors Q(x) nesting to the respective alloy Fermi surfaces as obtained f
rom the energy bands of a virtual-crystal band model. For BaBi1-xPbxO3
, Bi-Pb ordering waves are added by placing the Bi atoms onto those oc
tahedral sites that exhibit the largest breathing distortions. Using a
simple tight-binding Hamiltonian based on realistic energy-band calcu
lations, the model has been studied on large supercells, testing a mul
titude of lattice configurations. Experimental consequences are discus
sed.