  We present a calculation of radiative pion photoproduction in the framework
of covariant chiral perturbation theory with explicit $\Delta(1232)$ degrees of
freedom. The analysis is performed employing the small scale expansion scheme
adjusted for the $\Delta$ region. Depending on the channel, we include
contributions up to next-to-next-to-leading order. We fit the available
experimental data for the reaction $ \gamma p\to\gamma p\pi^0 $ and extract the
value of the $\Delta^+$ magnetic moment. Errors from the truncation of the
small scale expansion are estimated using the Bayesian approach. We compare our
results both with the previous studies within the $\delta$-expansion scheme and
with the $\Delta$-less theory. We also give predictions for radiative
charged-pion photoproduction.
