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In a recent work, it has been found that the suboptimum detectors that are based on Markov chain Monte Carlo (MCMC) simulation techniques perform significantly better than their sphere decoding (SD) counterparts. In this letter, we explore the sources of this difference and show that a modification to existing sphere decoders can result in some improvement in their performance, even though they still fall short when compared with the MCMC detector. We also present a novel SD detector that is an exact realization of max-log-MAP detector. We call this exact max-log SD detector. Comparison of the results of this detector with those of the max-log version of the MCMC detector reveals that the latter is near optimal.