  We present a new approach for setting initial Cauchy data for multiple black
hole spacetimes. The method is based upon adopting an initially Kerr-Schild
form of the metric. In the case of non-spinning holes, the constraint equations
take a simple hierarchical form which is amenable to direct numerical
integration. The feasibility of this approach is demonstrated by solving
analytically the problem of initial data in a perturbed Schwarzschild geometry.
