  We show that a proposed duality [arXiv:0711.0054] between infinitely coupled
gauge theories and superconformal field theories (SCFTs) with weakly gauged
flavor groups predicts the existence of new rank 1 SCFTs. These superconformal
fixed point theories have the same Coulomb branch singularities as the rank 1
E_6, E_7, and E_8 SCFTs, but have smaller flavor symmetry algebras and
different central charges. Gauging various subalgebras of the flavor algebras
of these rank 1 SCFTs provides many examples of infinite-coupling dualities,
satisfying an intricate set of consistency checks. They also provide examples
of N=2 conformal theories with marginal couplings but no weak-coupling limits.
