  The Wheeler-DeWitt equation for a class of Kantowski-Sachs like models is
completely solved. The generalized models include the Kantowski-Sachs model
with cosmological constant and pressureless dust. Likewise contained is a
joined model which consists of a Kantowski-Sachs cylinder inserted between two
FRW half--spheres. The (second order) WKB approximation is exact for the wave
functions of the complete set and this facilitates the product structure of the
wave function for the joined model. In spite of the product structure the wave
function can not be interpreted as admitting no correlations between the
different regions. This problem is due to the joining procedure and may
therefore be present for all joined models. Finally, the {s}ymmetric {i}nitial
{c}ondition (SIC) for the wave function is analyzed and compared with the ``no
bouindary'' condition. The consequences of the different boundary conditions
for the arrow of time are briefly mentioned.
