Let \(\Psi\) (x,y) denote the number of positive integers up to x and free of prime factors greater than y. Although \(\Psi\) (x,y) cannot be well approximated by a smooth function when y is small compared to x it is proved that it behaves locally more regular. Sharp estimates are given for \(\Psi\) (cx,y)/\(\Psi\) (x,y) in the range \(x\geq y\geq 4 \log x\), \(y\geq c\geq 1\).