  We use exponent pairs to establish the existence of many $x^a$-smooth numbers
in short intervals $[x-x^b,x]$, when $a>1/2$. In particular, $b=1-a-a(1-a)^3$
is admissible. Assuming the exponent-pairs conjecture, one can take
$b=(1-a)/2+\epsilon$. As an application, we show that $[x-x^{0.4872},x]$
contains many practical numbers when $x$ is large.
