  We study a driftless system on a three-dimensional manifold driven by two
scalar controls. We assume that each scalar control has an independent bound on
its modulus and we prove that, locally around every point where the controlled
vector fields satisfy some suitable nondegeneracy Lie bracket condition, every
time-optimal trajectory has at most five bang or singular arcs. The result is
obtained using first-and second-order necessary conditions for optimality.
