Minimum mean squared error (MMSE)-based soft iterative detection schemes have been widely considered for coded multiple antenna systems due to their high performance gain with reasonable complexity. This letter presents compact universal equations to estimate soft symbol values for 2^K -ary QAM and PSK schemes that can be applied to any MMSE-based iterative detection. The evaluation results investigated in this letter reveal that the proposed methods reduce the computational complexity by more than an order without degrading the performance.