The 2×2 MIMO profiles included in Mobile WiMAX specifications are Alamouti’s space-time code (STC) fortransmit diversity and spatial multiplexing (SM). The former has/nfull diversity and the latter has full rate, but neither of them has/nboth of these desired features. An alternative 2×2 STC, which is both full rate and full diversity, is the Golden code. It is the best known 2×2 STC, but it has a high decoding complexity. Recently, the attention was turned to the decoder complexity, this issue was/nincluded in the STC design criteria, and different STCs were/nproposed. In this paper, we first present a full-rate full-diversity/n2×2 STC design leading to substantially lower complexity of/nthe optimum detector compared to the Golden code with only a slight performance loss. We provide the general optimized form of this STC and show that this scheme achieves the diversitymultiplexing frontier for square QAM signal constellations. Then, we present a variant of the proposed STC, which provides a further decrease in the detection complexity with a rate reduction of 25% and show that this provides an interesting trade-off between the Alamouti scheme and SM.