  We investigate the origin of next-to-leading power corrections to the event
shapes thrust and $c$-parameter, at next-to-leading order. For both event
shapes we trace the origin of such terms in the exact calculation, and compare
with a recent approach involving the eikonal approximation and momentum shifts
that follow from the Low-Burnett-Kroll-Del Duca theorem. We assess the
differences both analytically and numerically. For the $c$-parameter both exact
and approximate results are expressed in terms of elliptic integrals, but near
the elastic limit it exhibits patterns similar to the thrust results.
