  We perform an analysis of the CMB temperature data taken by the Planck
satellite investigating if there is any significant deviation from cosmological
isotropy. We look for differences in the spectrum between two opposite
hemispheres and also for dipolar modulations. We propose a new way to avoid
biases due to partial-sky coverage by producing a mask symmetrized in antipodal
directions, in addition to the standard smoothing procedure. We also properly
take into account both Doppler and aberration effects due to our peculiar
velocity and the anisotropy of the noise, since these effects induce a
significant hemispherical asymmetry. We are thus able to probe scales all the
way to ell = 2000. After such treatment we find no evidence for significant
hemispherical anomalies (i.e. deviations are less than 1.5 sigma when summing
over all scales). Although among the larger scales there are sometimes higher
discrepancies, these are always less than 3 sigma. We also find results on a
dipolar modulation of the power spectrum. Along the hemispheres aligned with
the most asymmetric direction for 2 <= ell <= 2000 we find a 3.3 sigma
discrepancy when comparing to simulations. However, if we do not restrict
ourselves to Planck's maximal asymmetry axis, which can only be known a
posteriori, and compare Planck data with the modulation of simulations along
their respective maximal asymmetry directions, the discrepancy goes down to
less than 1 sigma (with, again, almost 3 sigma discrepancies in some low-ell
modes). We thus conclude that no significant power asymmetries seem to be
present in the full data set. Interestingly, without proper removal of Doppler
and aberration effects one would find spurious anomalies at high ell, between 3
sigma and 5 sigma. Even when considering only ell < 600 we find that the boost
is non-negligible and alleviates the discrepancy by roughly half-sigma.
