  In the standard inflationary scenario, primordial perturbations are
adiabatic. The amplitudes of most types of isocurvature perturbations are
generally constrained by current data to be small. If, however, there is a
baryon-density perturbation that is compensated by a dark-matter perturbation
in such a way that the total matter density is unperturbed, then this
compensated isocurvature perturbation (CIP) has no observable consequence in
the cosmic microwave background (CMB) at linear order in the CIP amplitude.
Here we search for the effects of CIPs on CMB power spectra to quadratic order
in the CIP amplitude. An analysis of the Planck temperature data leads to an
upper bound $\Delta_{\rm rms}^2 \leq 7.1\times 10^{-3}$, at the 68\% confidence
level, to the variance $\Delta_{\rm rms}^2$ of the CIP amplitude. This is then
strengthened to $\Delta_{\rm rms}^2\leq 5.0\times 10^{-3}$ if Planck
small-angle polarization data are included. A cosmic-variance-limited CMB
experiment could improve the $1\sigma$ sensitivity to CIPs to $\Delta^2_{\rm
rms} \lesssim 9\times 10^{-4}$. It is also found that adding CIPs to the
standard $\Lambda$CDM model can improve the fit of the observed smoothing of
CMB acoustic peaks just as much as adding a non-standard lensing amplitude.
