  Extending the results of an earlier article we give a complete description of
the asymptotically flat, conformally non-flat, static vacuum data which admit
non-trivial, asymptotically smooth conformal mappings onto other such data.
These data form a 3-parameter family which decomposes into 1-parameter families
of data which are conformal to each other. The data and the associated static
vacuum solutions are given explicitly in terms of elliptic and, in a special
case, elementary functions.
