Unique-word (UW) OFDM is a new multicarrier technique that was recently proposed in [1]. To construct the UW-OFDM signal, some carriers must be sacrificed to transmit redundant information – these carriers are called the redundant carriers. It turns out that the average redundant energy needed strongly depends on the positions of the redundant carriers. In this paper, we look for the redundant carrier placement that minimizes the average redundant energy – this needs an exhaustive search over all possible redundant carrier placements. Hence, the computational complexity to find the optimal redundant carrier distribution is very high. Therefore, we introduce a suboptimal redundant carrier placement – the quasi-uniform (QU) distribution, that is based on the results of the exhaustive search, and determines the positions of the redundant carriers at no computational cost. We show in this paper that the redundant energy needed for the proposed QU distribution is very close to the theoretical minimum average redundant energy.