  Laminar electrically conducting Couette flows with the hydrodynamically
stable quasi-Keplerian rotation profile and non-uniform conductivity are probed
for dynamo instability. In spherical geometry the equations for the poloidal
and the toroidal field components completely decouple, resulting in free decay,
regardless of the spatial distribution of the electric conductivity. In
cylindrical geometry the poloidal and toroidal components do not decouple, but
here also we do not find dynamo excitations for the cases that the electric
conductivity only depends on the radius or -- much more complex -- that it only
depends on the azimuthal or the axial coordinate. The transformation of the
plane-flow dynamo model of Busse \& Wicht (1992) to cylindrical or spherical
geometry therefore fails. It is also shown that even the inclusion of axial
flows of both directions does {\em not} support the dynamo mechanism. The
Elsasser toroidal-velocity antidynamo theorem, according to which dynamos
without any radial velocity component cannot work, is thus not softened by
non-uniform conductivity distributions.
