While there exist many techniques for finding the parameters that minimize an error function, only those methods that solely perform local computations are used in connectionist networks. The most popular learning algorithm for connectionist networks is the back-propagation procedure, which can be used to update the weights by the method of steepest descent. In this paper, we examine steepest descent and analyze why it can be slow to converge. We then propose four heuristics for achieving faster rates of convergence while adhering to the locality constraint. These heuristics suggest that every weight of a network should be given its own learning rate and that these rates should be allowed to vary over time. Additionally, the heuristics suggest how the learning rates should be adjusted. Two implementations of these heuristics, namely momentum and an algorithm called the delta-bar-delta rule, are studied and simulation results are presented.