We discuss the conditions under which the BRST operator of a W-string
can be written as the sum of two operators that are separately nilpote
nt and anticommute with each other. We illustrate our results with the
example of the non-critical W3-string. Furthermore, we apply our resu
lts to make a conjecture about a relationship between the spectrum of
a non-critical W(n)-string and a W(n-1)-string.