Abstract: A single-chain insulin analogue containing (i) diverse amino-acid substitutions at position A14; (ii) wild-type or variant residues at positions A8 and A14; and (ii) an engineered C-domain segment of lengths 4-6 containing a specific set of Alanine substitutions and/or deletions derived from the prototype C-domain sequence Glu-Glu-Gly-Pro-Arg-Arg. The analogue may otherwise be an analogue of a mammalian insulin, such as human insulin, may optionally include standard or non-standard modifications that (i) augment the stability of insulin, (ii) cause a shift in the isoelectric point to enhance or impair the solubility of the protein at neutral pH or (iii) reduce cross-binding of the protein to the Type I IGF receptor. Formulations of the above analogues at successive strengths U-100 to U-1000 in soluble solutions under acidic or neutral pH values (e.g., pH 3.0-4.2 and 6.5-7.8, respectively) and optionally in the presence of zinc ions at a molar ratio of 2.2-10 zinc ions per six insulin analogue monomers.