  We undertake a thorough search for signatures of sharp oscillatory features
in the WMAP9 power spectrum and bispectrum as well as in the Planck power
spectrum. For the first time, we carry out searches in both the power spectrum
and bispectrum simultaneously, employing well-defined look-elsewhere statistics
to assess significances in a rigorous manner. Developing efficient methods to
scan power spectrum likelihoods for oscillatory features, we present results
for the phenomenological bare sine and cosine modulations, allowing validation
against existing Planck Likelihood surveys, as well as templates that include
the correct sharp feature scaling. In particular, we study degeneracies between
feature and cosmological parameters. For frequencies beyond the scale set by
the acoustic peaks, the dependencies are realised through uninteresting
adjustments of the comoving distance to last scattering. Hence, it is
sufficient to keep cosmological parameters fixed and employ fast Gaussian
approximations to the likelihood as a function of the feature model amplitude.
In cases where results can be compared to the literature, our method shows
excellent agreement. We supplement results from the Planck Likelihood with an
analysis based on the Planck SMICA component separation map that, working on
the assumption that the component separation algorithm is reliable, allows for
the inclusion of a larger sky fraction. In principle, this allows us to place
the most stringent constraints to date on the amplitudes of feature models in
the temperature power spectrum. Invoking the WMAP bispectrum, we perform a
combined power spectrum and bispectrum survey. We use and slightly generalise
statistics developed in previous work to reliably judge the significance of
large feature model amplitude estimates. We conclude that our results are
entirely consistent with a featureless realisation of a Gaussian CMB.
