Abstract: The parametrization of adiabatic paths is optimal when tunnelling is minimized. Hamiltonian evolutions do not have such optimizers. However, dephasing Lindblad evolutions do. The optimizers are sim- ply characterized by an Euler-Lagrange equation and have a constant tunnelling rate along the path irrespective of the gap. I will show why Hamiltonian problem is ill-posed, introduce Lindblad evolutions and show how they regularize the problem.