Cross-efficiency　evaluation　is　a　commonly　used　approach　for　ranking　decision-making　units　(DMUs)　in　data　envelopment　analysis　(DEA).　The　weights　used　in　the　cross-efficiency　evaluation　may　sometimes　differ　significantly　among　the　inputs　and　outputs.　This　paper　proposes　some　alternative　DEA　models　to　minimize　the　virtual　disparity　in　the　cross-efficiency　evaluation.　The　proposed　DEA　models　determine　the　input　and　output　weights　of　each　DMU　in　a　neutral　way　without　being　aggressive　or　benevolent　to　the　other　DMUs.　Numerical　examples　are　tested　to　show　the　validity　and　effectiveness　of　the　proposed　DEA　models　and　illustrate　their　significant　role　in　reducing　the　number　of　zero　weights.　Journal　of　the　Operational　Research　Society　(2012)　63,　1079-1088.　doi:　10.1057/jors.2011.116　Published　online　9　November　2011