Insulin analogs comprising a non-native glycosylation site sequence are provided having high potency and specificity for the insulin receptor. In one embodiment a peptide sequence of greater than 18 amino acids is used as a linking moiety to link human insulin A and B chains, or analogs or derivatives thereof, to provide high potency single chain insulin analogs. In one embodiment the linking moiety comprises one or more glycosylation sites. Also disclosed are prodrug and conjugate derivatives of the insulin analogs.