An important parameter for several high breakdown regression algorithm estimators is the number of cases given weight one, called the coverage of the estimator. Increasing the coverage is believed to result in a more stable estimator, but the price paid for this stability is greatly decreased resistance to outliers. A simple modification of the algorithm can greatly increase the coverage and hence its statistical performance while maintaining high outlier resistance.
Olive, David J. and Hawkins, Douglas M. "Robust Regression with High Coverage." (Jul 2003).