A new region of superdeformed shapes with a pronounced triaxiality coexisti
ng with normal deformation exists for nuclei with N similar to 94 and Z sim
ilar to 71. Calculations with the Ultimate Cranker have revealed that triax
ial SD minima with gamma similar to +/-20 degrees are expected for all symm
etry groups (pi,alpha). In an odd-odd nucleus, the possibility exists to ex
ploit the various combinations of proton and neutron orbitals which are exp
ected to sample the triaxial minima differently A search for such structure
s was performed as one of the first Euroball experiments using the reaction
La-139(Si-29,4n) with thin self-supporting targets at a beam energy of 145
MeV, provided by the Legnaro XTU tandem accelerator The preliminary analys
is has provided a major extension of the known (normal deformed) level sche
me in Lu-164, in addition to similar to 7 new, presumably triaxial, SD band
s in Lu-164. These bands have dynamical moments of inertia similar to those
found in Lu-163,Lu-165. The new data are compared to expectations from cal
culations with the code "Ultimate Cranker".