  Inspection of the CM diagrams of globular clusters having similar heavy
element content shows that the luminosity of the red giant bump relative to the
turnoff (Delta V_{TO}^{bump}) differs by more than 0.1 mag between clusters
with different horizontal branch morphology. Unfortunately, careful
consideration of the data leaves us with only one pair (M3 and M13) of clusters
good for a quantitative discussion. For this pair we consider differences in
age and helium content as possible causes for the difference in Delta
V_{TO}^{bump}, and find more convincing support for the latter. A larger helium
content in M13 stars (Y~0.28 vs. Y~0.24) accounts for various CM diagram
features, such as the difference in the luminosity level of RR Lyr variables
and of the red giant bump with respect to the turnoff luminosity, and the
horizontal branch morphology. This enhanced helium can be tentatively
understood in the framework of self--enrichment by massive asymptotic giant
branch stars in the first ~100 Myr of the cluster life. A modest
self--enrichment can be present also in M3 and can be the reason for the still
unexplained presence of a not negligible number of luminous, Oosterhoff II type
RR Lyr variables. The hypothesis that a larger helium content is the second
parameter for clusters with very blue horizontal branch morphology could be
checked by an accurate set of data for more clusters giving turnoff, RR Lyrs
and bump magnitudes within a unique photometry.
