I will discuss the acceleration of first order methods for non smooth optimisation (examples include Forward-Backward, ADMM, Douglas Rachford and Primal-Dual). In the current literature, the most widely used form of acceleration is the ‘inertial technique’, and while there are improved performance guarantees for methods such as gradient descent and the Forward-Backward algorithm, in general, inertial can lead to a slow down in performance. We introduce a general framework for the acceleration of such methods motivated by the trajectory/structural properties of the sequences generated by such methods.