The problem of coverage is a fundamental issue in wireless sensor networks. In this article, we consider two subproblems: k-coverage contour evaluation and k-coverage rate deployment. The former aims to evaluate, up to k, the coverage level of any location inside a monitored area, while the latter aims to determine the locations of a given set of sensors to guarantee the maximum increment of k-coverage rate when they are deployed into the area. For the k-coverage contour evaluation problem, a nonuniform-grid-based approach is proposed.We prove that the computation cost of our approach is at most the square root of existing solutions. Based on our k-coverage contour evaluation scheme, a greedy k-coverage rate deployment scheme (k-CRD) is proposed, which is shown to be an order faster than existing studies for k-coverage rate deployment. The k-CRD can incorporate two different heuristics to further reduce its running time. Simulation results show that k-CRD with these heuristics can be significantly more time efficient without causing much degradation in the coverage rate of final deployment.