Disclosed are linkers containing a 2,3-disubstituted succinic group, or 2-monosubstituted, or 2,3-disubstituted fumaric or maleic group for conjugation of two or more compounds/cytotoxic agents per linker to a cell-binding molecule through bridge linking pairs of thiols on the cell-binding molecule, as well as methods of making such linkers, of using such linkers in making homogeneous conjugates, and of application of the conjugates in treatment of cancers, infections and autoimmune disorders.