  Let $\xi$ be an analytic bracket-generating distribution. We show that the
subspace of germs that are singular (in the sense of Control Theory) has
infinite codimension within the space of germs of smooth curves tangent to
$\xi$. We formalise this as an asymptotic statement about finite jets of
tangent curves. This solves, in the analytic setting, a conjecture of Y.
Eliashberg and N.M. Mishachev regarding an earlier claim by M. Gromov about the
microflexibility of the tangency condition.
  From these statements it follows, by an argument due to M. Gromov, that the
$h$-principle holds for maps and immersions transverse to $\xi$.
