The P3b component of ERPs has been proposed to reflect decisions or, alternatively, activation of stimulus-response links or, alternatively, to depend on stimulus processing only. These three views make different predictions about how difficulty of response selection will affect the oddball effect. In three experiments, frequent and rare targets were accompanied by ancillary stimuli. Large oddball-P3bs, evoked by rare targets, were greatly reduced when responses had to be selected by combining information from targets and ancillary stimuli. Difficult response selection with rare targets was also reflected by a large frontocentral negativity, which could be separated from P3b when intervals were varied between targets and ancillary stimuli, and, therefore, did not cause P3b reduction. It is concluded that the usual increase of P3b with rare task-relevant targets depends on the existence of readily available stimulus-response links.