  We introduce the notion of ``finite general representation type'' for a
finite-dimensional algebra, a property related to the ``dense orbit property''
introduced by Chindris-Kinser-Weyman. We use an interplay of geometric,
combinatorial, and algebraic methods to produce a family of algebras of wild
representation type but finite general representation type. For completeness,
we also give a short proof that the only local algebras of discrete general
representation type are already of finite representation type. We end with a
Brauer-Thrall style conjecture for general representations of algebras.
