Let (S,0) be a rational complex surface singularity with reduced
fundamental cycle, also known as a {\em minimal} singularity. Using a
fundamental result by M. Spivakovsky, we explain how to get a minimal
resolution of the discriminant curve for a generic projection of (S,0) onto
(\C^2,0) directly from the resolution graph of (S,0).Comment: February 2003. Submitted to CRA