Summary: Semantic paradoxes, like the Liar Paradox, are one of the best-known motivations for the dialetheists’ claim that there are true contradictions. Liar-like arguments arise in natural language and dialetheists argue that the Liar sentence is true and false, i.e., it bears a glut as its truth-value. However, in a recent paper, J. Beall [Analysis, Oxf. 75, No. 4, 573–584 (2015; Zbl 1369.03026)] argued that, by parallel reasoning, one should also be led from the resoures of natural language of triviality by the use of validity paradoxes (Curry-style paradoxes involving a pre-theoretical notion of validity). G. Priest [Australas. J. Log. 13, No. 5, 89–95 (2016; Zbl 1422.03011)] answers Beall’s challenge based on a typical move against Curry paradoxes: we avoid triviality by avoiding structural contraction, which is one of the steps in the derivation of triviality. We shall argue that this strategy poses some further difficulties for the dialetheist: i) it is hard for a dialetheist to motivate restriction of structural contraction; ii) structural contraction, if properly motivated, on the other hand, may lead one to avoid the Liar paradox too, and thus, the main motivation for the existence of gluts seems threatened; iii) the asymmetry in the treatment of paradoxes (take the Liar at face value, avoid the Curry) raises difficulties for the desideratum that pre-theoretical concepts should play a prominent role in motivating dialetheism.