  Normally one assumes isolated surface singularities to be normal. The purpose
of this paper is to show that it can be useful to look at nonnormal
singularities. By deforming them interesting normal singularities can be
constructed, such as isolated, non Cohen-Macaulay threefold singularities. They
arise by a small contraction of a smooth rational curve, whose normal bundle
has a sufficiently positive subbundle. We study such singularities from their
nonnormal general hyperplane section.
