  We apply the Weyl method, as sanctioned by Palais' symmetric criticality
theorems, to obtain those -highly symmetric -geometries amenable to explicit
solution, in generic gravitational models and dimension. The technique consists
of judiciously violating the rules of variational principles by inserting
highly symmetric, and seemingly gauge fixed, metrics into the action, then
varying it directly to arrive at a small number of transparent, indexless,
field equations. Illustrations include spherically and axially symmetric
solutions in a wide range of models beyond D=4 Einstein theory; already at D=4,
novel results emerge such as exclusion of Schwarzschild solutions in cubic
curvature models and restrictions on ``independent'' integration parameters in
quadratic ones. Another application of Weyl's method is an easy derivation of
Birkhoff's theorem in systems with only tensor modes. Other uses are also
suggested.
