In recent publications the use of lattice-reduction for signal detection in multiple antenna systems has been proposed. In this paper, we adopt these lattice-reduction-aided schemes to the MMSE criterion. We show that an obvious way to do this is infeasible and propose an alternative method based on an extended system model, which in conjunction with simple successive interference cancellation nearly reaches the performance of maximum-likelihood detection. Furthermore, we demonstrate that a sorted QR decomposition can significantly reduce the computational effort associated with lattice-reduction. Thus, the new algorithm clearly outperforms existing methods with comparable complexity.