In this paper, a closed-loop wireless communication system employing Quasi-Orthogonal Space-Time Block Codes (QOSTBCs) is presented, where the total available power can be suitably allocated to the four transmit antennas, considering a very low-complexity decoding scheme at the receiver side. After deriving a particular optimization problem concerning the optimal choice of the power weights, we prove that the best strategy in terms of error probability is to switch-off three out of the four transmit antennas under the requirement of symbolby-symbol maximum-likelihood decoding (MLD). Our proposed scheme requires a very low-data rate dedicated feedback link, since just one or two bits per block are sufficient for outperforming other existing closed-loop systems. The technique applies to all the well-known QOSTBCs with arbitrary number of receive antennas, while some special cases are taken indicatively for illustration purposes.