An insulin compound coupled to a modifying moiety having a formula: —X—R1—Y-PAG-Z—R  (Formula VI) where, X, Y and Z are independently selected linking groups and each is optionally present, and X, when present, is coupled to the insulin compound by a covalent bond, either R1 or R2 is is a lower alkyl, optionally including a carbonyl group, and when R1 is a lower alkyl, R2 is a capping group, and PAG is a linear or branched carbon chain incorporating one or more alkalene glycol moieties, and optionally incorporating one or more additional moieties selected from the group consisting of —S—, —O—, —N—, and —C(O)—, and where the modifying moiety has a maximum number of 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, or 25 heavy atoms.