  We investigate a set of cosmological models for which the primordial power
spectrum has a large-scale power deficit. The standard power-law spectrum is
subject to long-wavelength modifications described by some new parameters,
resulting in corrections to the anisotropies in the cosmic microwave
background. The new parameters are fitted to different data sets: temperature
only, temperature and polarization, the low-redshift determination of $H_0$,
and baryonic acoustic oscillations. We discuss the statistical significance of
the modified spectra, from both frequentist and Bayesian perspectives. Our
analysis suggests motivations for considering models that break scalar-tensor
consistency, or models with negligible power in the far super-Hubble limit. We
present what appears to be substantial evidence for a new scale around 350 Mpc
above which the primordial (scalar) power spectrum is sharply reduced by about
20%.
