Alternative Questions with “or not” (NAQ) convey a cornering effect, which is notfound with they polar counterparts (PQ). This effect has been claimed to consist of two parts(Biezma 2009): NAQs (i) cannot be used discourse-initially and (ii) they do not license followupquestions/subquestions. In this paper, we ask the following: Are both parts of corneringlinked to the same property of NAQs? Or do they reflect distinct linguistic phenomena? Weexplore the issue by comparing the behavior of NAQs to Complement Alternative Questions(CAQ), a type of question that, like NAQs, presents logically opposite alternatives but, unlikeNAQs, fully spells out the second one. Results from two experiments suggest that both parts ofcornering can instead be explained in terms of independent semantic and pragmatic principles,which operate beyond the domain of alternative questions.Keywords: Alternative Questions, cornering, discourse, focus, information structure.