A class of estimation procedures that are robust, relatively efficient, and yet computationally simple is proposed for the one- and two-sample location problems. Particular emphasis is placed on the problem of determining confidence intervals, a topic that has seen limited exposure in the literature. As a by-product, some interesting point estimates are obtained. A class of score functions that are ordinary step functions is considered for the location model. Point estimates and confidence intervals are obtained by inverting the corresponding rank statistics. Efficiency and robustness properties of the procedures are investigated. Simple computational schemes for the estimates and intervals are provided.