  We consider the effect of grey-body factors on the entanglement island
prescription for computing the entropy of an arbitrary subset of the Hawking
radiation of an evaporating black hole. When there is a non-trivial grey-body
factor, the modes reflected back into the black hole affect the position of the
quantum extremal surfaces at a subleading level with respect to the scrambling
time. The grey-body factor allows us to analyse the role of irreversibility in
the evaporation. In particular, we show that irreversibility allows multiple
saddles to dominate the entropy, rather than just two as expected on the basis
of Page's theorem. We show that these multiple saddles can be derived from a
generalization of Page's theorem that involves a nested temporal sequence of
unitary averages. We then consider how irreversibility affects the monogamy
entanglement problem.
