This paper investigates the design of precoders for single-user multiple-input multiple-output (MIMO) channels, and in particular for finite-alphabet signals. Based on an asymptotic expression for the mutual information of channels exhibiting line-of-sight components and rather general antenna correlations, a low-complexity iterative algorithm is devised that radically reduces the computational load of existing approaches with only minimal loss in performance. The complexity savings increase with the number of transmit antennas and with the cardinality of the signal alphabet, making it possible to support values thereof that were unwieldy in existing solutions. Most importantly, the proposed solution does not require instantaneous channel state information (CSI) at the transmitter, but only statistical CSI.