  The tension between the best fit parameters derived by the Planck team and a
number of other astronomical measurements suggests either systematics in the
astronomical measurements, systematics in the Planck data, the need for new
physics, or a combination thereof. We re-analyze the Planck data and find that
the $217\,\text{GHz}\times 217\,\text{GHz}$ detector set spectrum used in the
Planck analysis is responsible for some of this tension. We use a map-based
foreground cleaning procedure, relying on a combination of 353 GHz and 545 GHz
maps to reduce residual foregrounds in the intermediate frequency maps used for
cosmological inference. For our baseline data analysis, which uses 47% of the
sky and makes use of both 353 and 545 GHz data for foreground cleaning, we find
the $\Lambda$CDM cosmological parameters $\Omega_c h^2 = 0.1170 \pm 0.0025$,
$n_s = 0.9686 \pm 0.0069$, $H_0 = 68.0 \pm 1.1\,\mathrm{km}
\mathrm{s}^{-1}\mathrm{Mpc}^{-1}$, $\Omega_b h^2 = 0.02197 \pm 0.00026$, $\ln
10^{10}A_s = 3.082 \pm 0.025$, and $\tau = 0.090 \pm 0.013 $. While in broad
agreement with the results reported by the Planck team, these revised
parameters imply a universe with a lower matter density of
$\Omega_m=0.302\pm0.015$, and parameter values generally more consistent with
pre-Planck CMB analyses and astronomical observations. We compare our cleaning
procedure with the foreground modeling used by the Planck team and find good
agreement. The difference in parameters between our analysis and that of the
Planck team is mostly due to our use of cross-spectra from the publicly
available survey maps instead of their use of the detector set cross-spectra
which include pixels only observed in one of the surveys. We show evidence
suggesting residual systematics in the detector set spectra used in the Planck
likelihood code, which is substantially reduced for our spectra.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology;High Energy Physics - Theory