  In this paper, we propose an improved method for directly calculating
double-copy-compatible tree numerators in (super-)Yang-Mills and
Yang-Mills-scalar theories. Our new scheme gets rid of any explicit dependence
on reference orderings, restoring a form of crossing symmetry to the
numerators. This in turn improves the computational efficiency of the
algorithm, allowing us to go well beyond the number of external particles
accessible with the reference order based methods. Motivated by a parallel
study of one-loop BCJ numerators from forward limits, we explore the
generalization to include a pair of fermions. To improve the accessiblity of
the new algorithm, we provide a Mathematica package that implements the
numerator construction. The structure of the computation also provides for a
straightforward introduction of minimally-coupled massive particles potentially
useful for future computations in both classical and quantum gravity.
