Summary: Let \(\gamma,\tau : [a,b] \to \mathbb{R}^{k+1}\) be a couple of Lipschitz maps such that \(\gamma' = \pm|\gamma'| \tau\) almost everywhere in \([a,b]\). Then \(\gamma ([a,b])\) is a \(C^2\)-rectifiable set, namely it may be covered by countably many curves of class \(C^2\) embedded in \(\mathbb{R}^{k+1}\). As a consequence, projecting the rectifiable carrier of a one-dimensional generalized Gauss graph provides a \(C^2\)-rectifiable set.