MIMO spatial multiplexing systems are attracting a lot of attention because of their high spectral effiencies. Maximum Likelihood Detection (MLD) is known to be the optimal signal detection method for MIMO spatial multiplexing systems in terms of bit error rate (BER). However, the main drawback of MLD is its high complexity. In this paper, to reduce the computational complexity of MLD and to attain good BER in MIMO spatial multiplexing systems, we propose the minimum mean square error (MMSE)-MLD that combines MMSE detection and MLD according to the estimated SINR from each transmit antenna. We also propose the ordered successive MMSE detection (OSD)-MLD that combines OSD and MLD according to the estimated SINR from the transmit antennas. Simulation results show that the proposed MMSE-MLD and OSD-MLD can attain almost identical BER to that of MLD but with less complexity.