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Adaptive modulation is a technique which alters constellation size depending on channel condition to achieve highspeed data transmission. However, the well-known modulation schemes transmitting odd bits per symbol, such as 8-ary phase shift keying (PSK) and cross quadrature amplitude modulation (cross QAM), are generally not considered as a candidate for the adaptive use due to their inherent power inefficiency. In this paper, we address three triangular quadrature amplitude modulations (TQAMs), i.e. regular, optimum and suboptimum TQAMs, to improve transmission efficiency for such odd-bit modulations. We suggest optimum and suboptimum bit stream mapping methods and a simple and optimum detection method for the proposed constellations. Analysis and simulation show that optimum and suboptimum TQAMs can provide the power gains of 1.80 dB and 1.64 dB over the conventional 8-ary PSK at a target symbol error rate of 10-6 while maintaining low detection complexity.