  We give a simple proof of the fact that a finite measure $\mu$ on the unit
disk is a Carleson measure for the Dirichlet space if it satisfies the Carleson
one-box condition $\mu(S(I))=O(\phi(|I|))$, where $\phi:(0,2\pi]\to(0,\infty)$
is an increasing function such that $\int_0^{2\pi}(\phi(x)/x)\,dx<\infty$. We
further show that the integral condition on $\phi$ is sharp.
