How should central banks optimally aggregate sectoral inflation rates in the presence of imperfect labor mobility across sectors? We study this issue in a two-sector New-Keynesian model and show that a lower degree of sectoral labor mobility, ceteris paribus, increases the optimal weight on inflation in a sector that would otherwise receive a lower weight. We analytically and numerically find that, with limited labor mobility, adjustment to asymmetric shocks cannot fully occur through the reallocation of labor, thus putting more pressure on wages, causing inefficient movements in relative prices, and creating scope for central banks intervention. These findings challenge standard central banks practice of computing sectoral inflation weights based solely on sector size, and unveil a significant role for the degree of sectoral labor mobility to play in the optimal computation. In an extended estimated model of the U.S. economy, featuring customary frictions and shocks, the estimated inflation weights imply a decrease in welfare up to 10 percent relative to the case of optimal weights.