Dialetheism is the view according to which some contradictions (i.e., statements of the form, A and not-A) are true. In this paper, I discuss three strategies to block dialetheism: (i) Contradictions cannot be true because some theories of truth preclude them from emerging. (ii) Contradictions cannot be true because we cannot see what it is like to perceive them. Although that does not undercut the possibility that there are true contradictions that we cannot perceive, it makes their introduction a genuine cost. (iii) Contradictions cannot be true because if they were, we would end up sliding down into believing that everything is true (trivialism). Even if the dialetheist is not committed to that slippery slope, it is crucial that the dialetheist establishes that trivialism is unacceptable; but it is not clear how that could be done successfully. Graham Priest has considered these strategies (in his Doubt Truth to be a Liar), but I argue that none of his responses successfully block them.