Cloud Radio Access Network (Cloud-RAN) has recently been proposed as a promising network architecture to maintain both profitability and quality of service of the ever-growing existing networks. This paper provides an extended optimization study of improving the performance of Cloud-RAN targeting minimized consumed power for the network. The minimization problem can be formulated as a Joint RRH selection and power minimization beamforming problem. We adapt a proposed greedy selection algorithm to decrease the number of active Remote Radio Heads (RRHs) and to optimize the transmitted power from RRHs to end users maintaining heterogeneous users' QoS requirements. A heuristics-driven approach has been proposed and applied to the optimization problem to further reach better optimum solutions of power consumption and to reduce the problem complexity. Simulation results coupled with a statistical analysis show that more reduction in both power consumption and complexity have been reached.