Insulin conjugates comprising an insulin molecule covalently attached to at least one bi-dentate linker having two arms, each arm independently attached to a ligand comprising a saccharide and wherein at least one ligand of the linker is fucose are disclosed. The insulin conjugates display a pharmacokinetic (PK) and/or pharmacodynamic (PD) profile that is responsive to the systemic concentrations of a saccharide such as glucose or alpha-methylmannose even when administered to a subject in need thereof in the absence of an exogenous multivalent saccharide-binding molecule such as Con A.