An appealing explanation for the Planck data is provided by inflationary models with a singular non-canonical kinetic term: a Laurent expansion of the kinetic function translates into a potential with a nearly shift-symmetric plateau in canonical fields. The shift symmetry can be broken at large field values by including higher-order poles, which need to be hierarchically suppressed in order not to spoil the inflationary plateau. The herefrom resulting corrections to the inflationary dynamics and predictions are shown to be universal at lowest order and possibly to induce power loss at large angular scales. At lowest order there are no corrections from a pole of just one order higher and we argue that this phenomenon is related to the well-known extended no-scale structure arising in string theory scenarios. Finally, we outline which other corrections may arise from string loop effects.