For traditional methods of observed-score equating with anchor-test designs, such as chain and poststratification equating, it is difficult to satisfy the criteria of equity and population invariance. Their equatings are therefore likely to be biased. The bias in these methods was evaluated against a simple local equating method in which the anchor-test score was used as a proxy of the proficiency measured by the test and the equating was conditional on this score. The results showed substantial bias for the two traditional methods under a variety of conditions but much smaller bias for the local method. In addition, unlike the traditional methods, the local method appeared to be quite robust with respect to changes in the difficulty and accuracy of the two tests that were equated. But like these methods, it appeared to be sensitive to a decrease in the accuracy of the anchor test as a proxy of the ability measured by the tests.