The Chen-Stein method of Poisson approximation has been used to establ
ish theorems about comparison of two DNA or protein sequences. The mos
t useful result for sequence alignment applies to alignment scoring wi
th no gaps. However, there has not been a valid method to assign stati
stical significance to alignment scores with gaps. In this paper we ex
tend Poisson approximation techniques using the Aldous clumping heuris
tic to a practical method of estimating statistical significance.