  The increase in luminosity as a star evolves on the red-giant branch is
interrupted briefly when the hydrogen-burning shell reaches the vicinity of the
composition discontinuity left behind from the first convective dredge-up. The
non-monotonic variation of luminosity causes an accumulation of stars, known as
the `bump', in the distribution of stars in the colour-magnitude diagrams of
stellar clusters, which has substantial diagnostic potential. Here I present
numerical results on this behaviour and discuss the physical reason for the
luminosity variation, with the goal of strengthening the understanding of
origin of the phenomenon and hence of its diagnostic potential.
