In operational equating, frequency estimation (FE) equipercentile equating is often excluded from consideration when the old and new groups have a large ability difference. This convention may, in some instances, cause the exclusion of one competitive equating method from the set of methods under consideration. In this report, we study the possibility of using the FE equating method when the group ability difference is large. Three situations are identified: (a) a situation in which neither the two forms nor the observed conditional distributions are very different so that the FE equating assumptions are likely to hold, and FE equating is recommended; (b) a situation in which forms are not very different, but the observed conditional distributions are different, so that FE equating is not recommended; and (c) a situation in which forms are very different, but the observed conditional distributions are not different, so that FE equating is not recommended. Statistical analysis procedures for comparing distributions are provided. An application of equating to a large-scale admission test is discussed to illustrate the proposed methodology.