The scope and limits of unconscious processing are a matter of ongoing debate. Lately, continuous flash suppression (CFS), a technique for suppressing visual stimuli, has been widely used to demonstrate surprisingly high-level processing of invisible stimuli. Yet, recent studies showed that CFS might actually allow low-level features of the stimulus to escape suppression and be consciously perceived. The influence of such low-level awareness on high-level processing might easily go unnoticed, as studies usually only probe the visibility of the feature of interest, and not that of lower-level features. For instance, face identity is held to be processed unconsciously since subjects who fail to judge the identity of suppressed faces still show identity priming effects. Here we challenge these results, showing that such high-level priming effects are indeed induced by faces whose identity is invisible, but critically, only when a lower-level feature, such as color or location, is visible. No evidence for identity processing was found when subjects had no conscious access to any feature of the suppressed face. These results suggest that high-level processing of an image might be enabled by-or co-occur with-conscious access to some of its low-level features, even when these features are not relevant to the processed dimension. Accordingly, they call for further investigation of lower-level awareness during CFS, and reevaluation of other unconscious high-level processing findings.