  We propose a simplification for the IR-resummation scheme of Senatore and
Zaldarriaga, and also include its next-to-leading order corrections coming from
the tree-level three-point function of the long displacement field. First we
show that the new simplified formula shares the same properties of the
resummation of Senatore and Zaldarriaga. In Fourier space, the IR-resummed
power spectrum has no residual wiggles and the two-loop calculation matches the
non-linear power spectrum of the Dark Sky simulation at $z=0$ up to
$k\simeq0.34\,h\,\text{Mpc}^{-1}$ within cosmic variance. Then, we find that
the additional subleading terms (although parametrically infrared-enhanced)
modify the leading-order IR-resummed correlation function only in a marginal
way, implying that the IR-resummation scheme can robustly predict the shape of
the BAO peak.
