Two methods of local linear observed-score equating for use with anchor-test and single-group designs are introduced. In an empirical study, the two methods were compared with the current traditional linear methods for observed-score equating. As a criterion, the bias in the equated scores relative to true equating based on Lord's (1980) definition of equity was used. The local method for the anchor-test design yielded minimum bias, even for considerable variation of the relative difficulties of the two test forms and the length of the anchor test. Among the traditional methods, the method of chain equating performed best. The local method for single-group designs yielded equated scores with bias comparable to the traditional methods. This method, however, appears to be of theoretical interest because it forces us to rethink the relationship between score equating and regression.