The quadrupole moments Q(0) of five superdeformed bands in Ce-131,Ce-1
32 have been established using the Doppler-shift attenuation method; f
or the first time, we can compare relative deformations of yrast and e
xcited bands in different nuclei to an accuracy of similar or equal to
(5-7)%. Four of the five bands have very similar deformations, while t
he excited band in Ce-131 has a somewhat larger quadrupole moment. Imp
ortant new information is presented on the shape-driving force of the
vi(13/2) orbital, the stability of the second minimum with respect to
particle excitations, the relative deformations of identical bands, th
e nature of the sidefeeding, and the time scale of the decay process.