A well-known problem of using radial projection in Data Envelopment Analysis (DEA) is that the solution may be only weakly efficient—not necessarily efficient. Our aim is to overcome this drawback by developing a lexicographic approach to projecting radially any unit onto the efficient frontier—not only onto the weakly efficient frontier. The approach is based on the idea to apply radial projection by stepwise dropping component(s) from the radial projection vector until the efficient frontier is reached. The approach has two main differences compared to the traditional approach: (1) the target unit on the efficient frontier is found in the spirit of radial projection and (2) the (in)efficiency score is not necessarily the same for all controllable variables. A numerical illustration and an empirical example are used to demonstrate the approach.