Immunoconjugates comprising a targeting agent selectively targeting cell- surface expressed syndecan-1 and at least one effector molecule as well as in vitro and in vivo methods of using those immunocomjugates are disclosed. The effector molecule may have, in its native form, high non-selective cytotoxicity, but substantially no non-selective cytotoxicity when part of said immunoconjugate. Targeting agents include the antibody B-B4 as well as other agents that bind cell- surface expressed syndecan-1.
