  Turning on N=2 supersymmetry-preserving relevant operators in a 4-dimensional
N=2 superconformal field theory (SCFT) corresponds to a complex deformation
compatible with the rigid special Kahler geometry encoded in the low energy
effective action. Field theoretic consistency arguments indicate that there
should be many distinct such relevant deformations of each SCFT fixed point.
Some new supersymmetry-preserving complex deformations are constructed of
isolated rank 1 SCFTs. We also make predictions for the dimensions of certain
Higgs branches for some rank 1 SCFTs.
