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The constellation-to-ground coverage problem is a basic and important problem in satellite applications. The grid-point approach (GPA) is one of the most commonly used approaches to solving this problem. However, this approach also has some serious drawbacks. A group of strategies that can improve or overcome the drawbacks of this approach are proposed. The spatial and temporal characteristics of the GPA were analyzed, and a strategy that can compute the upper and lower bounds of the result was given. This strategy can not only acquire the result but can also yield the error range of the result. In addition, a strategy that uses low-precision results to compute a high-precision result is proposed. Simulation experiments of different types of coverage problems were conducted, and the results show that these strategies are effective.