The minimization of expended energy for unicast and broadcast communication between nodes in a wireless network has been studied mostly as a path optimization problem without particular regard for the traffic load demands. In this paper, we consider the call admission problem whereby given a traffic load (described as source-destination rate demands) the required expended energy is minimized. In addition, we explicitly model bandwidth capacity constraints. The capacity constraints reflect the fact that, from the perspective of a single node, traffic includes data that the nodes originate and forward, as well as traffic they receive and is of no interest to them. This last class of traffic is unavoidable due to the transmission radius of nearby stations. Under the assumption that the MAC protocol behaves in an ideal fashion, we consider two centralized algorithms that attempt to admit the given load and we remark on their relative performance, especially with respect to their energy consumption and blocking (connection rejection) rate.