We study the effects of the X-point configuration on ELM triggering peeling and ballooning modes by using fixed boundary equilibria and modifying the plasma shape to approach the limit of a true X-point. The current driven pure peeling modes are asymptotically stabilised by the X-point while the stabilising effect on ballooning modes depends on the poloidal location of the X-point. The coupled peeling-ballooning modes experience the elimination of the peeling component as the X-point is introduced. This can significantly affect the edge stability diagrams used to analyse the ELM triggering mechanisms.