A method of targeted random mutagenesis has been used to investigate the informational content of 25 residue positions in two alpha-helical regions of the N-terminal domain of lambda repressor. Examination of the functionally allowed sequences indicates that there is a wide range in tolerance to amino acid substitution at these positions. At positions that are buried in the structure, there are severe limitations on the number and type of residues allowed. At most surface positions, many different residues and residue types are tolerated. However, at several surface positions there is a strong preference for hydrophilic amino acids, and at one surface position proline is absolutely conserved. The results reveal the high level of degeneracy in the information that specifies a particular protein fold.