  Harmonic superspace can be used to construct higher derivative terms in N=2
supersymmetric effective actions despite the infinite redundancy in their
description due to the infinite number of auxiliary fields. We are able to
write down all of the 3- and 4-derivative terms on the Higgs, Coulomb, and
mixed branches, modulo the possible existence of superspace Chern-Simons-like
terms, which we discuss. Many of the terms we find are holomorphic, and at
least one is shown to not receive quantum corrections.
