The purpose of this study was to evaluate the use of adjoined and piecewise linear approximations (APLAs) of raw equipercentile equating functions as a postsmoothing equating method. APLAs are less familiar than other postsmoothing equating methods (i.e., cubic splines), but their use has been described in historical equating practices of large‐scale testing programs. This study used simulations to evaluate APLA equating results and compare these results with those from cubic spline postsmoothing and from several presmoothing equating methods. The overall results suggested that APLAs based on four line segments have accuracy advantages similar to or better than cubic splines and can sometimes produce more accurate smoothed equating functions than those produced using presmoothing methods.