The invention provides heterodimer bispecific antigen-binding molecules that include a first polypeptide that does not include an IgG CH1 domain and a second polypeptide where there is at least one mutation in the IgG CH3 domain that abolishes the ability of the second polypeptide to bind CH3-specific affinity media such that the first and second polypeptides have different affinities with respect to CH1 and CH3 specific affinity reagents that allows rapid isolation by differential binding. The invention also provides bispecific antibodies that have CH1 and CH3 regions with different affinities with respect to affinity reagents that allows rapid isolation by differential binding. The invention also concerns bispecific antibodies which are heterodimers of two IgG heavy chains that differ by at least two amino acids that allow for rapid isolation based on a differential affinity of one mutated heavy chain and a second mutated heavy chain toward two different affinity reagents.