  In this paper we present a method for producing asymptotic estimates for the
number of integers in a given S having only ``small'' prime factors. The
conditions that need to be verified are simpler than those required by other
methods, and we apply our result to give an easy proof of a result which says
that dense subsets A and B of {1,2,...,x} always produce asymptotically the
expected number of x^r - smooth sums a+b, where a in A and b in B. Recall that
a number n is said to be y-smooth if all its prime divisors are at most y.
