Opportunistic grids are distributed computing infrastructures that harvest the idle computing cycles of computing resources geographically distributed. In these grids, the demand for resources is typically bursty. During bursts of resource demand, many grid resources are required, but on other times they remain idle for long periods. If the resources are kept powered on even when they are neither processing their owners workload nor grid jobs, their exploitation is not efficient in terms of energy consumption. One way to reduce the energy consumed in these idleness periods is to place the computers that form the grid in a “sleeping” mode which consumes less energy. We evaluated two sleeping strategies, denoted: standby and hibernate. Resources that comprise an opportunistic grid are normally very heterogeneous, and differ enormously on their processing power and energy consumption. It opens the possibility of implementing scheduling strategies that take energy-efficiency into account. We consider scheduling in two different levels. Firstly, how to choose which machine should be woken up, if several options are available. Secondly, how to decide which tasks to schedule to the available machines. In summary, our results presented a significant reduction in energy consumption, surpassing 80% in a scenario when the amount of resources in the grid was high. Moreover, this comes with limited impact on the response time of the applications.