We study Smoothed Online Convex Optimization, a version of online convex\noptimization where the learner incurs a penalty for changing her actions\nbetween rounds. Given a $\\Omega(\\sqrt{d})$ lower bound on the competitive ratio\nof any online algorithm, where $d$ is the dimension of the action space, we ask\nunder what conditions this bound can be beaten. We introduce a novel\nalgorithmic framework for this problem, Online Balanced Descent (OBD), which\nworks by iteratively projecting the previous point onto a carefully chosen\nlevel set of the current cost function so as to balance the switching costs and\nhitting costs. We demonstrate the generality of the OBD framework by showing\nhow, with different choices of "balance," OBD can improve upon state-of-the-art\nperformance guarantees for both competitive ratio and regret, in particular,\nOBD is the first algorithm to achieve a dimension-free competitive ratio, $3 +\nO(1/\\alpha)$, for locally polyhedral costs, where $\\alpha$ measures the\n"steepness" of the costs. We also prove bounds on the dynamic regret of OBD\nwhen the balance is performed in the dual space that are dimension-free and\nimply that OBD has sublinear static regret.\n