Modified glucagon peptides are disclosed having enhanced potency at the glucagon receptor relative to native glucagon. Further modification of the glucagon peptides by forming lactam bridges or the substitution of the terminal carboxylic acid with an amide group produces peptides exhibiting glucagon/GLP-1 receptor co-agonist activity. The solubility and stability of these high potency glucagon analogs can be further improved by modification of the polypeptides by pegylation, substitution of carboxy terminal amino acids, or the addition of a carboxy terminal peptide selected from the group consisting of SEQ ID NO: 26 (GPSSGAPPPS), SEQ ID NO: 27 (K-RNRNNIA) and SEQ ID NO: 28 (KRNR).