We describe a generic approach to assemble correctly two heavy and two light chains, derived from two existing antibodies, to form human bivalent bispecific IgG antibodies without use of artificial linkers. Based on the knobs-into-holes technology that enables heterodimerization of the heavy chains, correct association of the light chains and their cognate heavy chains is achieved by exchange of heavy-chain and light-chain domains within the antigen binding fragment (Fab) of one half of the bispecific antibody. This “crossover” retains the antigen-binding affinity but makes the two arms so different that light-chain mispairing can no longer occur. Applying the three possible “CrossMab” formats, we generated bispecific antibodies against angiopoietin-2 (Ang-2) and vascular endothelial growth factor A (VEGF-A) and show that they can be produced by standard techniques, exhibit stabilities comparable to natural antibodies, and bind both targets simultaneously with unaltered affinity. Because of its superior side-product profile, the CrossMab^CH1-CL was selected for in vivo profiling and showed potent antiangiogenic and antitumoral activity.