This article presents a complexity and delay analysis of Parallel Sorting Algorithms (PSA) in K-best Sphere-Decoder (K-best SD) receivers in slow-flat Rayleigh fading channels for MIMO (Multiple-Input Multiple-Output) systems. The K-best SD algorithm is a strategic Near-Optimal Spatial-Multiplexing MIMO (SM-MIMO) demodulation solution (due to its trade-off between Bit-Error-Rate performance and algorithmic complexity) that requires sorting procedures for symbol-decoding purposes. Unfortunately, sorting represents a critical data throughput bottleneck for K-best SD architectures. PSA alleviate this situation by providing suitable implementations of sorting algorithms easily adapted to K-best SD architectures. Several versions of the Bubble-Sort (BS) and the Batcher-Sort (BtchS) algorithms are considered for this analysis.