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Currently used adaptive equalizers for the minimization of mean-square error in digital communications commonly employ a fixed-step-size gradient-search procedure. The algorithm to be described here employs variable step sizes designed to minimize the error after a specified number of iterations. The resultant convergence rate provides considerable improvement over the fixed-step-size approach. Bounds on the variance, valid for large signal-to-noise ratios, indicate that the new algorithm not only converges faster, but also has a smaller variance asymptotically than the present algorithm for moderate intersymbol interference and the same variance asymptotically for large intersymbol interference. Computer simulation studies have verified these results.