The correlation of peak intensities of solar energetic particle (SEP) events with the speeds of the associated coronal mass ejections (CMEs) is understood to be a result of SEP acceleration at shocks driven by the CMEs. However, the peak SEP intensities associated with CMEs of a given speed vary over ~ 4 orders of magnitude. We examine a database of 71 E>10 MeV SEP events observed with the GOES satellite to determine whether enhanced ambient SEP intensities at the times of the CMEs and/or variations among SEP event spectra contribute to the large range of peak SEP event intensities. A statistical analysis shows that enhanced ambient SEP intensities may be a contributing factor to the range of SEP events of higher peak intensities, probably by providing sources of energetic seed particles for the shock acceleration process. Another factor is the variation of energy spectra among the SEP events, which generally have harder spectra with increasing peak intensities. The observed increase of peak SEP intensities and hardening of peak SEP spectra with increasingly westward solar source regions is only a minor factor in the range of SEP peak intensities in the CME speed correlation. ¿ 2001 American Geophysical Union