The control of the topology of a network makes it possible for the network nodes to reduce their power of transmission while ensuring that network connectivity is preserved. This paper explains the need for energy consumption control in Wireless Mesh Networks (WMNs) and proposes a Local Minimum Shortest-Path Tree (LM-SPT) algorithm for topology control for the WMNs. The algorithm is distributed with each node using only the information gathered locally to determine its own transmission power. The implementation is done in two phases. The construction of a minimum local shortest-path tree is first done. The removal of all unidirectional links is then done. The performance of the algorithm is demonstrated via several simulation tests. The resultant network topology preserves network connectivity in addition to possessing other desirable features such as: (1) reduction in the average node degree, (2) evenly distributed power consumption among the nodes as well as (3) a reduced total power consumption leading to longer connectivity periods.