  Radiative transfer simulation is an important tool that allows us to generate
synthetic images of various astrophysical objects. In the case of complex
three-dimensional geometries, a Monte Carlo-based method that simulates photon
packages as they move through and interact with their environment is often
used. Previous studies have shown, in the regime of high optical depths, that
the required number of simulated photon packages strongly rises and estimated
fluxes may be severely underestimated. In this paper we identify two problems
that arise for Monte Carlo radiative transfer simulations that hinder a proper
determination of flux: first, a mismatch between the probability and weight of
the path of a photon package and second, the necessity of simulating a wide
range of high scattering orders. Furthermore, we argue that the peel-off method
partly solves these problems, and we additionally propose an extended peel-off
method. Our proposed method improves several shortcomings of its basic variant
and relies on the utilization of precalculated sphere spectra. We then combine
both peel-off methods with the Split method and the Stretch method and
numerically evaluate their capabilities as opposed to the pure
Split$\,\&\,$Stretch method in an infinite plane-parallel slab setup. We find
that the peel-off method greatly enhances the performance of these simulations;
in particular, at a transverse optical depth of $\tau_{\rm max}=75$ our method
achieved a significantly lower error than previous methods while simultaneously
saving ${>}95\%$ computation time. Finally, we discuss the inclusion of
polarization and Mie-scattering in the extended peel-off method, and argue that
it may be necessary to equip future Monte Carlo radiative transfer simulations
with additional advanced pathfinding techniques.
