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Multimode quantized precoding (QP) can provide full diversity gain or high capacity gain by adapting the number of substreams, as well as the precoding matrix, according to the instantaneous channel condition with low-rate feedback. Conventional multimode QP (MM-QP), however, does not consider the adaptive rate allocation among substreams; thus, it cannot have the additional gain by adaptive modulation. Furthermore, it is computationally complex since exhaustive matrix inversions are required to determine the optimal mode. In this paper, we propose an efficient MM-QP system that improves the performance of a conventional system in terms of error rate and has a lower computational complexity than the conventional system. First, we define the rate-partitioning vector as the mode and control the rate among substreams and the number of substreams according to the channel instantaneous condition. Second, to reduce the computational complexity for the receiver to determine the optimal mode, the simplified mode-selection technique using estimates of the modal metric is proposed. In the proposed mode-selection technique, the optimal mode can be obtained by several multiplication and division operations. Finally, the mode-reduction technique eliminating the less-frequently used modes is proposed, which leads to a significant reduction of the feedback information with negligible performance loss. In numerical experiments, it was verified that the proposed MM-QP system gives a better error-rate performance than the conventional system, with much less computational complexity for the same amount of feedback information.