  Under a nondegeneracy condition, we show that an equiregular sub-Riemannian
manifold of step size $r$ admits a canonical, $V$-rigid complement defined from
the sub-Riemannian data that is preserved the by action of sub-Riemannian
isometries. We explore how the existence of such a complement relates to
results from the literature and study the step size 2 case in more detail.
