The P3b component of human event-related EEG potentials is larger with rare than frequent task-relevant stimuli. In a previous study, this oddball effect was much reduced when stimulus-response (S-R) mappings were still undefined at stimulus presentation (being later provided by response prompts). This reduction may reflect P3b's dependence on transmitted information which might be any relevant information (informational value hypothesis) or, more specifically, information about how to respond (S-R link hypothesis). To distinguish between these two hypotheses and clarify their differences from classical stimulus evaluation hypothesis, we added a second dimension by presenting colored letters, with both colors and letters varying between a rare and a frequent alternative. Response prompts, presented half a second later, were, in different blocks, constant or variable across trials with respect to S-R mapping and with respect to the relevant dimension (color or letter). With partial information, when only one of these two factors is known at stimulus presentation (by being constant across trials), the hypotheses differ in their predictions. The oddball effect will be abolished according to S-R link hypothesis because knowledge of both factors is needed to determine the response, but will only be reduced according to informational value hypothesis and be fully maintained according to stimulus evaluation hypothesis. In fact, oddball effects only occurred with knowledge of both factors, i.e., if both the relevant dimension and its mapping to responses were constant across trials. These results confirm the preeminent role of knowledge about responses for eliciting P3.