An equalizer based on the minimum mean-square error (MSE) criterion, but with direct solution of the resulting equations, is described. The direct solution is based on the algorithms devised by Levinson and Trench. With the availability of large-scale integration (LSI) bipolar computing elements, these algorithms are competitive with iterative procedures. A method is considered for the estimation of the required parameters, and for automatic adaption to a changing channel. It is shown that the delay can be adjusted to achieve minimum MSE with respect to that parameter. Simulations undertaken show the robust performance of the algorithm, and that the equalizer performance is not adversely affected by operation in decision-directed mode.