||Free Disposal Hull (FDH) is one of the tools in the theoretical and empirical work on the measurement of productive efficiency. Excluding linear combinations of extremal observations to construct this reference technology entails that many of the observations belonging to an evaluated dataset are labeled efficient by this method. Few researchers have sought to improve the discrimination power of FDH. Van Puyenbroeck [H. Tulkens, On FDH efficiency analysis: some methodological issues and applications to retail, banking, courts and urban transit, Journal of Productivity Analysis 4 (1993) 183-210] modified standard FDH method by using Andersen and Petersen [N. Adler, L. Friedman, Z. Siunuany-Stern, Review of ranking methods in the data envelopment analysis context, European Journal of Operational Research, 140 (2002) 249-265], referred to A%P FDH. Jahanshahloo et al. [J. Doyle, R. Green, Efficiency and cross-efficiency in DEA: derivation, meanings and uses, Journal of Operational Research Society 45 (5) (1994) 567-578] used 0-1 linear programming (LP), referred to 0-1 LP FDH to find FDH-efficient units. The purpose of this paper is two-folds: to propose MAJ FDH, similar to in spirit as the ranking method in data envelopment analysis by Mehrabian et al. [S. Mehrabian, M.R. Alirezaee, G.R. Jahanshahloo, A complete efficiency ranking of decision making units in data envelopment analysis, Communicational Optimization and Applications 14 (1999) 261-266] that may thus be used to discriminate between FDH-efficient units and to examine the tie-breaking ability of A%P FDH, 0-1 LP FDH, and MAJ FDH by using three numerical examples. Results of the comparisons show: (i) as the number of DMU, input and output is small where all of input and output levels are positive, the A%P FDH can provide a full ranking; (ii) as the number of DMU, input and output is small where some of input and output levels are equal to zero, none of three extended FDH methods can provide a full ranking; and (iii) as the number of DMU, input and output are increased where all of input and output levels are positive, it seems that ranking by MAJ FDH is more precise than other FDH methods.