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Compensated isocurvature perturbations (CIP), where the baryon and cold darkmatter perturbations cancel, do not cause total matter isocurvatureperturbation. Consequently, at the linear order in the baryon density contrast$\Delta$, CIP is not detectable by the CMB power spectra. At the second orderCIP smoothes the power spectra in a similar manner as lensing, causing adegeneracy between the CIP variance $\Delta^2_{rms}=<\Delta^2>$ and lensingparameter $A_L$. We show that the CMB lensing data breaks this degeneracy.Nested sampling of the LCDM+CIP(+$A_L$) model, the Planck 2015 temperature,polarization, and lensing data give $\Delta^2_{rms}=0.0069\pm0.0030$ at 68% CL.A non-zero value is favored at 2.3$\sigma$. CIP with $\Delta^2_{rms}=0.007$improves the bestfit $\chi^2$ by 3.6 compared to the adiabatic LCDM model. Incontrast, although the temperature data favor $A_L=1.22$, allowing $A_L\ne1$does not improve the joint fit, since the lensing data disfavor $A_L\ne1$.Indeed, CIP provides a rare example of a simple model, which can reduce thePlanck lensing anomaly by fitting well simultaneously the high multipoletemperature and lensing data, as well as the polarization data. Finally, wederive forecasts for future satellite missions (LiteBIRD proposal to JAXA andExploring Cosmic Origins with CORE proposal to ESA's M5 call). Due to itscoarse angular resolution, LiteBIRD is not able to improve the constraints onCIP or $A_L$, but CORE-M5 approaches the cosmic variance limit and improves theCIP constraint to $\Delta^2_{rms}<0.0006\ (0.0014)$ at 68% (95%) CL, which is 9times better than the current trispectrum based upper bound and 6 times betterthan obtained from the simulated Planck data. In addition, CORE-M5 willexquisitely distinguish between CIP and $A_L$. No matter whether CIP is allowedfor or not, the uncertainty of the lensing parameter will be$\sigma(A_L)=0.012$.

Power Spectra Based Planck Constraints on Compensated Isocurvature, and Forecasts for LiteBIRD and CORE Space Missions