Emerging wireless telecommunication systems, including the terrestrial LMDS (Local Multipoint Distribution System) and next-generation communication satellite systems (e.g., SpacewaySM, et al.) are driven by economics to require a burst-transmission protocol for their return links (i.e., subscriber-to-hub or subscriber-to-satellite links). Limited spectral bandwidth to support these return links demands that they achieve high spectrum efficiency, measured in terms of bps/Hz (bits-per-second-per-Hertz). High-order modulations offer practical spectrum-efficient solutions for continuous links, but technical difficulties associated with phase- coherent demodulation of high-order burst signals have previously precluded these modulations as a viable option. In fact, state-of-art burst signal demodulation is currently limited to differentially-detected QPSK (DQPSK). Although so- called block-coherent demodulators generate acceptable symbol- error rates, they introduce such strong symbol-to symbol correlation as to preclude efficient soft-decision decoding. In summary, new wireless links demand burst modems with bandwidth-efficiency and power-efficiency superior to currently available technology. SiCOM research has developed a practical burst demodulator compatible with both high-order modulations and soft-decision maximum-likelihood decoding. This paper describes the capabilities and characterizes the performance of this revolutionary demodulator. In particular, detailed performance comparisons are provided between the current state-of-art burst demodulator/decoder, using DQPSK and Reed-Solomon FEC (forward error correction), and SiCOM's new burst demodulator using 8PSK with concatenated TCM (trellis-coded modulation) and Reed-Solomon FEC. For ATM (asynchronous transfer mode) cell transfer, with identical link constraints, (i.e., signal-to-noise ratio, bandwidth, and bit-error rate), the new modem supports fully 25% higher information transfer rates. For message traffic with less- critical latency constraints, message-specific interleaving easily provides orders-of-magnitude improvement in data quality over the DQPSK/RS approach, with identical bandwidth and SNR (signal-to-noise ratio).