We identify new entangled motifs in proteins that we call complex lassos. Lassos arise in proteins with disulfide bridges (or in proteins with amide linkages), when termini of a protein backbone pierce through an auxiliary surface of minimal area, spanned on a covalent loop. We find that as much as 18% of all proteins with disulfide bridges in a non-redundant subset of PDB form complex lassos, and classify them into six distinct geometric classes, one of which resembles supercoiling known from DNA. Based on biological classification of proteins we find that lassos are much more common in viruses, plants and fungi than in other kingdoms of life. We also discuss how changes in the oxidation/reduction potential may affect the function of proteins with lassos. Lassos and associated surfaces of minimal area provide new, interesting and possessing many potential applications geometric characteristics not only of proteins, but also of other biomolecules.