In the very interesting paper under review, the authors prove Hölder continuity up to the boundary for the gradient of solutions to some fully-nonlinear, degenerate elliptic equations, with degeneracy coming from the gradient. Precisely, let \(u\) be a viscosity solution of the Dirichlet problem \[ \begin{cases} |\nabla u|^\alpha \big( F(D^2u)+h(u)\cdot \nabla u\big)=f & \text{in}\;\Omega,\\ u=\varphi & \text{on}\;\partial\Omega, \end{cases} \] where \(\Omega\subset\mathbb{R}^N\) is a bounded \(C^2\)-smooth domain, \(\alpha\geq0,\) \(F\) is uniformly elliptic, \(h,f\in C(\overline{\Omega})\) and \(\varphi\in C^{1,\beta_0}(\partial\Omega).\) The main result of the paper asserts existence of an exponent \(\beta,\) depending on the data of the problem, and a constant \(C=C(\beta)\) such that \[ \|u\|_{C^{1,\beta}(\overline{\Omega})}\leq C \left( \|u\|_{L^{\infty}({\Omega})}+ \|\varphi\|_{C^{1,\beta_0}({\partial\Omega})}+ \|f\|_{L^{\infty}({\Omega})}^{\frac{1}{1+\alpha}} \right). \]