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Numerical relativity codes now being developed will evolve initial datarepresenting colliding black holes at a relatively late stage in the collision.The choice of initial data used for code development has been made on the basisof mathematical definitiveness and usefulness for computational implementation.By using the ``particle limit'' (the limit of an extreme ratio of masses ofcolliding holes) we recently showed that the standard choice is not a goodrepresentation of astrophysically generated initial data. Here we show that,for the particle limit, there is a very simple alternative choice that appearsto give excellent results. That choice, ``convective'' initial data is, roughlyspeaking, equivalent to the start of a time sequence of parameterized solutionsof the Hamiltonian constraint; for a particle in circular orbit, it is theinitial data of the steady state solution on any hypersurface. Theimplementation of related schemes for equal mass holes is discussed.Comment: 10 pages, REVTEX, 14 PS fig

Improved initial data for black hole collisions