  We present an alternative approach to setting initial data in general
relativity. We do not use a conformal decomposition, but instead express the
3-metric in terms of a given unit vector field and one unknown scalar field. In
the case of axisymmetry, we have written a program to solve the resulting
nonlinear elliptic equation. We have obtained solutions, both numerically and
from a linearized analytic method, for a general perturbation of Schwarzschild.
