A hetero-dimeric protein comprising a first and a second single-chain protein, wherein said first single-chain protein comprises a first amino acid sequence consisting of (from the N- to the C-terminus): (ia) a first VL domain, (iia) a first polypeptide linker, and (iiia) a second VL domain, and wherein said second single-chain protein comprises a second amino acid sequence consisting of (from the N- to the C-terminus): (ib) a first VH domain, (iib) a second polypeptide linker, and (iiib) a second VH domain, and wherein said first VL domain forms a first cognate pair of variable domains with specificity to a first target antigen with either said first or said second VH domain, and said second VL domain forms a second cognate pair of variable domains with specificity to a second target antigen with the other of said VH domains, wherein one of said target antigens is human serum albumin and the other said target antigen is human CD3, wherein at least one of said first or said second single-chain protein further comprises (iv) at least one additional domain as third functional domain that is fused via a third polypeptide linker to said first or said second amino acid sequence, wherein said functional domain is a proteinaceous domain having a predefined function, particularly an enzymatic activity or specific binding to a cognate ligand, wherein each polypeptide linker consists of a chain of amino acid residues linked by peptide bonds, and wherein said first and said second single-chain proteins do not comprise an immunoglobulin constant domain. wherein said first single-chain protein comprises a first amino acid sequence consisting of (from the N- to the C-terminus): (ia) a first VL domain, (iia) a first polypeptide linker, and (iiia) a second VL domain, and (ia) a first VL domain, (iia) a first polypeptide linker, and (iiia) a second VL domain, and wherein said second single-chain protein comprises a second amino acid sequence consisting of (from the N- to the C-terminus): (ib) a first VH domain, (iib) a second polypeptide linker, and (iiib) a second VH domain, and (ib) a first VH domain, (iib) a second polypeptide linker, and (iiib) a second VH domain, and wherein said first VL domain forms a first cognate pair of variable domains with specificity to a first target antigen with either said first or said second VH domain, and said second VL domain forms a second cognate pair of variable domains with specificity to a second target antigen with the other of said VH domains, wherein one of said target antigens is human serum albumin and the other said target antigen is human CD3, wherein at least one of said first or said second single-chain protein further comprises (iv) at least one additional domain as third functional domain that is fused via a third polypeptide linker to said first or said second amino acid sequence, wherein said functional domain is a proteinaceous domain having a predefined function, particularly an enzymatic activity or specific binding to a cognate ligand, wherein each polypeptide linker consists of a chain of amino acid residues linked by peptide bonds, and wherein said first and said second single-chain proteins do not comprise an immunoglobulin constant domain.