  Compensated isocurvature perturbations (CIPs) are primordial fluctuations
that balance baryon and dark-matter isocurvature to leave the total matter
density unperturbed. The effects of CIPs on the cosmic microwave background
(CMB) anisotropies are similar to those produced by weak lensing of the CMB:
smoothing of the power spectrum, and generation of non-Gaussian features.
Previous work considered the CIP effects on the CMB power-spectrum but
neglected to include the CIP effects on estimates of the lensing potential
power spectrum (though its contribution to the non-Gaussian, connected, part of
the CMB trispectrum). Here, the CIP contribution to the standard estimator for
the lensing potential power-spectrum is derived, and along with the CIP
contributions to the CMB power-spectrum, Planck data is used to place limits on
the root-mean-square CIP fluctuations on CMB scales, $\Delta_{\rm rms}^2(R_{\rm
CMB})$. The resulting constraint of $\Delta_{\rm rms}^2(R_{\rm CMB}) < 4.3
\times 10^{-3}$ using this new technique improves on past work by a factor of
$\sim 3$. We find that for Planck data our constraints almost reach the
sensitivity of the optimal CIP estimator. The method presented here is
currently the most sensitive probe of the amplitude of a scale-invariant CIP
power spectrum placing an upper limit of $A_{\rm CIP}< 0.017$ at 95% CL. Future
measurements of the large-scale CMB lensing potential power spectrum could
probe CIP amplitudes as low as $\Delta_{\rm rms}^2(R_{\rm CMB}) = 8 \times
10^{-5}$ ($A_{\rm CIP} = 3.2 \times 10^{-4}$).
