Protein and DNA are generally represented by sequences of letters. In a number of circumstances simplified alphabets (where one or more letters would be represented by the same symbol) have proved their potential utility in several fields of bioinformatics including searching for patterns occurring at an unexpected rate, studying protein folding and finding consensus sequences in multiple alignments. The main issue addressed in this paper is the possibility of finding a general approach that would allow an exhaustive analysis of all the possible simplified alphabets, using substitution matrices like PAM and BLOSUM as a measure for scoring.