This paper addresses the optimal rate allocation problem in overlay content distribution for efficient utilization of limited bandwidths. We systematically present a series of optimal rate allocation strategies by dividing our discussions into four typical scenarios. Based on application-specific requirements, these scenarios reflect the contrast between elastic and streaming content distribution, with either per-link or per-node capacity constraints. In each scenario, we show that the optimal rate allocation problem can be formulated as a linear optimization problem, which can be solved efficiently in a fully distributed fashion. In simulations, we investigate the convergence of our distributed algorithms in both static and dynamic networks, and demonstrate their efficiency. Key words: Overlay Network, Rate Allocation, Optimization