  An analytically tractable model is introduced which exhibits both, a
glass--like freezing transition, and a collection of double--well
configurations in its zero--temperature potential energy landscape. The latter
are generally believed to be responsible for the anomalous low--temperature
properties of glass-like and amorphous systems via a tunneling mechanism that
allows particles to move back and forth between adjacent potential energy
minima. Using mean--field and replica methods, we are able to compute the
distribution of asymmetries and barrier--heights of the double--well
configurations {\em analytically}, and thereby check various assumptions of the
standard tunneling model. We find, in particular, strong correlations between
asymmetries and barrier--heights as well as a collection of single--well
configurations in the potential energy landscape of the glass--forming system
--- in contrast to the assumptions of the standard model. Nevertheless, the
specific heat scales linearly with temperature over a wide range of low
temperatures.
