  Biasing or importance sampling is a powerful technique in Monte Carlo
radiative transfer, and can be applied in different forms to increase the
accuracy and efficiency of simulations. One of the drawbacks of the use of
biasing is the potential introduction of large weight factors. We discuss a
general strategy, composite biasing, to suppress the appearance of large weight
factors. We use this composite biasing approach for two different problems
faced by current state-of-the-art Monte Carlo radiative transfer codes: the
generation of photon packages from multiple components, and the penetration of
radiation through high optical depth barriers. In both cases, the
implementation of the relevant algorithms is trivial and does not interfere
with any other optimisation techniques. Through simple test models, we
demonstrate the general applicability, accuracy and efficiency of the composite
biasing approach. In particular, for the penetration of high optical depths,
the gain in efficiency is spectacular for the specific problems that we
consider: in simulations with composite path length stretching, high accuracy
results are obtained even for simulations with modest numbers of photon
packages, while simulations without biasing cannot reach convergence, even with
a huge number of photon packages.
