Lattice Reduction (LR) has been proposed as a method to enhance the performance of MIMO detectors such as ZF, MMSE and V-BLAST. Until recently, the application of LR to the superior K-Best tree-search detection algorithm was not practical due to the significant increase in complexity of K-Best as a result of the distortion of tree symmetry caused by LR. However, in our recently published work we developed an innovative K-Best algorithm to accommodate tree-asymmetry with no additional complexity. In this work, we build on this result and perform a detailed analysis of the effect of various LR algorithms on the performance of LR-aided K-Best. We show that LLL and Seysen provide equivalent performance enhancement, however, LLL displays a lower computational complexity and thus is more suitable for LR-aided K-Best. In this work we also show that the application of LR to K-Best allows a large reduction of the K value while maintaining its near-ML performance. For 64-QAM MIMO detection, this leads to about 70% reduction in the complexity of the K-Best detector.