Pictures in a rapid serial visual presentation (RSVP) stream are better remembered when they are simultaneously presented with targets of an unrelated detection task than when they are presented with distractors. However, it is unclear whether this so-called "attentional boost effect" depends on the intentionality of encoding. While there are studies suggesting that the attentional boost effect even occurs when encoding is incidental, there are several methodological issues with these studies, which may have undermined the incidental encoding instructions. The present study (N = 141) investigated the role of the intentionality of encoding with an improved experimental design. Specifically, to prevent a spill-over of intentional resources to the pictures in the RSVP stream, the speed of the stream was increased (to four pictures per second) and each picture was presented only once during the course of the experiment. An attentional boost effect was only found when encoding was intentional but not when encoding was incidental. Interestingly, memory performance for incidentally encoded pictures was nevertheless substantially above chance, independently of whether images were presented with search-relevant targets or distractors. These results suggest that the attentional boost effect is a memory advantage that occurs only under intentional encoding conditions, and that perceptual long-term memory representations are formed as a natural product of perception, independently of the presence of behaviorally relevant events.