—Statistical detectors that are based on Markov chain Monte Carlo (MCMC) simulators have emerged as promising low-complexity solutions to both multiple-input multipleoutput (MIMO) and code division multiple access (CDMA) communication systems. While these types of detectors achieve unprecedented near capacity performance, i.e., when operated in low signal-to-noise ratio (SNR) regime, they exhibit a serious problem at medium to high SNR regimes, referred to as the “stalling” problem. In this paper, we investigate the sources of this degradation and propose a new search strategy called constrained MCMC to remedy the issue of stalling.