This paper investigates the syntax of negative fragment answers in Modern Irish, in particular those that involve Demonic Negation (DemNeg), which are constituted by the negative marker dheamhan, literally 'demon', and an adjacent XP. Following Merchant (2004) and Holmberg (2016), it is assumed that both fragment answers and answers to yes-no questions are fully clausal structures which are followed by an elided copy of the question. After a description of the strategies that are employed in Irish for answers to yes-no questions (Responsive Ellipsis, consisting in a repetition of the verb of the question) and to constituent questions, a syntax of non-elliptical DemNeg is provided for 'bare DemNeg' (in which the marker appears in the left periphery without an adjacent XP) and for DemNeg+XP. It is argued that dheamhan is base-generated in a left-peripheral NegP, above FocP. The XP that is found at the right of the negative marker is moved to SpecFocP from below, after which fragment ellipsis takes place. DemNeg+XP is thus not a case of constituent negation, but rather the linear sequence of a left-peripheral NegP and a focussed constituent. It is demonstrated via the licensing of polarity items that dheamhan has wide scope over the entire sentence, and not just over the adjacent XP, which is why fragments based on DemNeg constitute felicitous answers to yes-no questions. Finally, some observations are made on the incompatibility between demonic fragments and Responsive Ellipsis, which is due to the principle of MaxElide, and on a last-resort strategy for fragment answers based on bare DemNeg, whereby an anaphoric element which is co-referential with the elided clause is inserted in SpecFocP in order to trigger fragment ellipsis.