A list sphere decoder (LSD) can be used to approximate the optimal maximum a posteriori (MAP) detector for the detection of multiple-input multiple-output (MIMO) signals. In this paper, we consider two LSD algorithms with different search methods and study some algorithm design choices which relate to the performance and computational complexity of the algorithm. We show that by limiting the dynamic range of log-likelihood ratio, the required LSD list size can be lowered, and, thus, the complexity of the LSD algorithm is decreased. We compare the real and the complex-valued signal models and their impact on the complexity of the algorithms. We show that the real-valued signal model is clearly the less complex choice and a better alternative for implementation. We also show the complexity of the sequential search LSD algorithm can be reduced by limiting the maximum number of checked nodes without sacrificing the performance of the system. Finally, we study the complexity and performance of an iterative receiver, analyze the tradeoff choices between complexity and performance, and show that the additional computational cost in LSD is justified to get better soft-output approximation.