  We present a systematic study of N=1 supersymmetric gauge theories which are
in the Coulomb phase. We show how to find all such theories based on a simple
gauge group and no tree-level superpotential. We find the low-energy solution
for the new theories in terms of a hyperelliptic Seiberg-Witten curve. This
work completes the study of all N=1 supersymmetric gauge theories where the
Dynkin index of the matter fields equals the index of the adjoint (mu=G), and
consequently all theories for which mu<G.
