  While the general question of whether every closed embedding of an affine
line in affine $3$-space can be rectified remains open, there have been several
partial results proved by several different means. We provide a new approach,
namely constructing (strongly) residual coordinates, that allows us to give new
proofs of all known partial results, and in particular generalize the results
of Bhatwadekar-Roy and Kuroda on embeddings of the form $(t^n,t^m,t^l+t)$.
