Topology control is a well-known strategy to save energy and extend the lifetime of wireless sensor networks. It consists of topology construction and topology maintenance algorithms. While topology construction builds a reduced topology, topology maintenance changes the reduced topology when the current one is no longer optimal. The selection of an appropriate topology maintenance technique is rarely included in the evaluation of topology control solutions, even though the impact of such decision in the lifetime of the network (in terms of number of nodes or coverage) has been shown before. This paper makes two important contributions. First, it introduces a new topology construction algorithm called A3Cov, based on the A3 protocol, which increases the coverage ratio considerably compared to the original version. Second, the A3Cov protocol is evaluated jointly with four topology maintenance techniques to determine the influence of the different maintenance schemes on the area coverage and the network lifetime. The results show that the dynamic global topology maintenance techniques with A3Cov provide the best coverage and network lifetime for a substantially longer period of time compared to the ACOS protocol.