Abstract : Approximately half of the large-scale coronal waves identified in images obtained by the Extreme-Ultraviolet Imaging Telescope (EIT) on the Solar and Heliospheric Observatory from 1997 March to 1998 June were associated with small solar flares with soft X-ray intensities below C class. The probability of a given flare of this intensity having an associated EIT wave is low. For example, of ~8,000 B-class flares occurring during this 15 month period, only 1% were linked to EIT waves. These results indicate the need for a special condition that distinguishes flares with EIT waves from the vast majority of flares that lack wave association. Various lines of evidence, including the fact that EIT waves have recently been shown to be highly associated with coronal mass ejections (CMEs), suggest that this special condition is a CME. A CME is not a sufficient condition for a detectable EIT wave, however, because we calculate that 5 times as many front-side CMEs as EIT waves occurred during this period, after taking the various visibility factors for both phenomena into account. In general, EIT wave association increases with CME speed and width.