  The recursive method of Berends and Giele to compute tree-level gluon
amplitudes is revisited using the framework of ten-dimensional super
Yang-Mills. First we prove that the pure spinor formula to compute SYM tree
amplitudes derived in 2010 reduces to the standard Berends-Giele formula from
the 80s when restricted to gluon amplitudes and additionally determine the
fermionic completion. Second, using BRST cohomology manipulations in
superspace, alternative representations of the component amplitudes are
explored and the Bern-Carrasco-Johansson relations among partial tree
amplitudes are derived in a novel way. Finally, it is shown how the
supersymmetric components of manifestly local BCJ-satisfying tree-level
numerators can be computed in a recursive fashion.
