  We present new recursion relations for tree amplitudes in gauge theory that
give very compact formulas. Our relations give any tree amplitude as a sum over
terms constructed from products of two amplitudes of fewer particles multiplied
by a Feynman propagator. The two amplitudes in each term are physical, in the
sense that all particles are on-shell and momentum conservation is preserved.
This is striking, since it is just like adding certain factorization limits of
the original amplitude to build up the full answer. As examples, we recompute
all known tree-level amplitudes of up to seven gluons and show that our
recursion relations naturally give their most compact forms. We give a new
result for an eight-gluon amplitude, A(1+,2-,3+,4-,5+,6-,7+,8-). We show how to
build any amplitude in terms of three-gluon amplitudes only.
