Single chain insulin analogs are provided having high potency and specificity for the insulin receptor. As disclosed herein optimally sized linking moieties can be used to link human insulin A and B chains, or analogs or derivatives thereof, wherein the carboxy terminus of the B25 amino acid of the B chain is linked to the amino terminus of the A1 amino acid of the A chain via the intervening linking moiety. In on embodiment the linking moiety comprises a polyethylene glycol of 6-16 monomer units and in an alternative embodiment the linking moiety comprises a non-native amino acid sequence derived form the IGF-1 C-peptide and comprising at least 8 amino acids and no more than 12 amino acid in length. Also disclosed are prodrug and conjugate derivatives of the single chain insulin analogs.