We investigate a new Follow the Perturbed Leader (FTPL) algorithm for online structured prediction problems. We show a regret bound which is comparable to the state of the art of FTPL algorithms and is comparable with the best possible regret in some cases. To better understand FTPL algorithms for online structured learning, we present a lower bound on the regret for a large and natural class of FTPL algorithms that use logconcave perturbations. We complete our investigation with an online shortest path experiment and empirically show that our algorithm is both statistically and computationally efficient.