In this paper, we propose two simple signal detectors that are based on successive interference cancellation (SIC) for time-reversal space-time block codes to combat intersymbol interference in frequency-selective fading environments. The main idea is to treat undetected symbols and noise together as Gaussian noise with matching mean and variance and use the already-detected symbols to help current signal recovery. The first scheme is a simple SIC signal detector whose ordering is based on the channel powers. The second proposed SIC scheme, which is denoted parallel arbitrated SIC (PA-SIC), is a structure that concatenates in parallel a certain number of SIC detectors with different ordering sequences and then combines the soft output of each individual SIC to achieve performance gains. For the proposed PA-SIC, we describe the optimal ordering algorithm as a combinatorial problem and present a low-complexity ordering technique for signal decoding. Simulations show that the new schemes can provide a performance that is very close to maximum-likelihood sequence estimation (MLSE) decoding under time-invariant conditions. Results for frequency-selective and doubly selective fading channels show that the proposed schemes significantly outperform the conventional minimum mean square error-(MMSE) like receiver and that the new PA-SIC performs much better than the proposed conventional SIC and is not far in performance from the MLSE. The computational complexity of the SIC algorithms is only linear with the number of transmit antennas and transmission rates, which is very close to the MMSE and much lower than the MLSE. The PA-SIC also has a complexity that is linear with the number of SIC components that are in parallel, and the optimum tradeoff between performance and complexity can be easily determined according to the number of SIC detectors.