  We extend and improve the modeling and analysis of large-amplitude, sharp
inflationary steps for second order corrections required by the precision of
the Planck CMB power spectrum and for arbitrary Dirac-Born-Infeld sound speed.
With two parameters, the amplitude and frequency of the resulting oscillations,
step models improve the fit by $\Delta \chi^2 = -11.4$. Evidence for
oscillations damping before the Planck beam scale is weak: damping only
improves the fit to $\Delta \chi^2 = -14.0$ for one extra parameter, if step
and cosmological parameters are jointly fit, in contrast to analyses which fix
the latter. Likewise, further including the sound speed as a parameter only
marginally improves the fit to $\Delta \chi^2 = -15.2$ but has interesting
implications for the lowest multipole temperature and polarization anisotropy.
Since chance features in the noise can mimic these oscillatory features, we
discuss tests from polarization power spectra, lensing reconstruction and
squeezed and equilateral bispectra that should soon verify or falsify their
primordial origin.
