A measure of sequence similarity, dt, not requiring prior sequence alignment gave correct results for a variety of computer-generated model sequences without and with gaps for all degrees of substitution, s. Measure d was the squared Euclidean distance between vectors of counts of t-tuplets of characters in the two sequences. In models without gaps and without Needleman-Wunsch alignment, average d was very closely equal to twice average conventional mismatch counts, m. In these models one of each of the conditions on the Jukes-Cantor model was violated in turn: (1) both descendant lineages receive the same number of substitutions, (2) all sites are equally likely to be substituted, (3) all different replacement characters are equally likely to be chosen, and (4) all original characters are equally likely to be substituted. In Jukes-Cantor models with gaps Needleman-Wunsch alignment was necessarily performed, a procedure that generally produced incorrect values of m. For these models average d was found to be very closely equal to twice the average m estimated from the known value of s using the inverted Jukes-Cantor formula.