  We consider a Brownian functional $F=g\bigl(\int_0^T \eta(s) dW_s\bigr)$ with
$g \in L_2(\gamma)$ and a singular deterministic $\eta$. We deduce the
$L_2$-convergence rate for the approximation $F^{(n)} = E F + \int_0^T
\phi^{(n)}(s) dW_s$ for a class of piecewise constant predictable integrands
$\phi^{(n)}$ from the fractional smoothness of $g$ quantified by Besov spaces
and the rate of singularity of $\eta$.
