  We substantially refine the theory of singular principal bundles introduced
in a former paper. In particular, we show that we need only honest singular
principal bundles in our compactification. These are objects which carry the
structure of a rational principal bundle in the sense of Ramanathan. Moreover,
we arrive at a much simpler semistability condition. In the case of a
semisimple group, this is just the Gieseker-version of Ramanathan's
semistability condition for the corresponding rational principal $G$-bundle.
