In this talk, we will discuss regularity results for a class of degenerate, fully nonlinear elliptic equations with arbitrary nonhomogeneous degeneracy laws. We prove that, under suitable conditions on the degeneracy laws, viscosity solutions are locally continuously differentiable. Our proof relies on improvement of flatness techniques, combined with an alternative recursive algorithm for renormalizing the approximating solutions, which links our model to the homogeneous, fully nonlinear, uniformly elliptic equation.