  Exact Solov'ev equilibria for arbitrary plasma cross-sections are calculated
using a constrained least-squares method. The boundary, with or without
$X$-points, can be specified with an arbitrarily large number of constraints to
ensure an accurate representation. Thus, the order of the polynomial basis
functions in the homogeneous solution of the Grad-Shafranov equation becomes an
independent parameter determined only by the accuracy requirements of the
overall solution. Examples of exact, highly-shaped equilibria are presented.
