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 \sim 0.28 vs. Y \sim 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 \sim 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 .