We describe the construction of suboptimal trajectories of the problem of a planar motion with bounded derivative of the curvature and we prove their suboptimality. `Suboptimal' means longer than the optimal by no more than a constant depending only on the bound $B$ for the curvature's derivative. The initial and final coordinates, curvatures and tangent angles are given. The tangent angle and the curvature of the path are assumed to be continuous. The bound $B$ and the distance $d$ between the initial and final points satisfy an inequality of the kind $d\gg 1/\sqrtB$.