Effective Lenstra-Lenstra-Lovász (ELLL) algorithm is a common low-complexity lattice reduction (LR) technique adopted in LR-aided successive interference cancellation (SIC) multiple-input multiple-output (MIMO) detectors. However, the original ELLL algorithm is undesirable for hardware implementation since the number and the sequence of ELLL iterations are not deterministic. To address these issues, some fixed-complexity ELLL (fcELLL) algorithms have recently been proposed. In this paper, we propose two new fcELLL algorithms to further improve the efficiency of existing fcELLL algorithms by eliminating unnecessary iterations, such that the fcEL-LL algorithm exhibits faster convergence and lower computational complexity. Compared to the existing fcELLL algorithms, simulations show that the proposed fcELLL algorithms can save up to 39%-48% complexity for 8 × 8 MIMO systems without performance loss.