In this paper, I modify and augment my LFG-XLE analysis of negation in Hungarian proposed in Laczkó (2014b) by (i) developing an account of the special uses of negative particles (ii) capturing their interaction with negative polarity items (iii) presenting a formal treatment of suppletive negative variants of the copula. In addition, I argue for a particular distribution of labour in my approach for the three standard XLE devices for handling negation phenomena across languages.