  We obtain the holographic complexity of an evaporating black hole in the
semi-classical RST model of two-dimensional dilaton gravity, using a volume
prescription that takes into account the higher-dimensional origin of the
model. For classical black holes, we recover the expected late time behaviour
of the complexity, but new features arise at the semi-classical level. By
considering the volume inside the stretched horizon of the evolving black hole,
we obtain sensible results for the rate of growth of the complexity, with an
early onset of order the black hole scrambling time followed by an extended
period where the rate of growth tracks the shrinking area of the stretched
horizon as the black hole evaporates.
