We construct a price index with weights on the prices of different PCE goods chosen to minimize the welfare costs of nominal distortions: a cost-of-nominal-distortions index (CONDI). We compute these weights in a multisector New Keynesian model with time-dependent price setting, calibrated using U.S. data on the dispersion of price stickiness and labor shares across sectors. We find that the CONDI weights mostly depend on price stickiness and are less affected by the dispersion in labor shares. Moreover, CONDI stabilization leads to negligible welfare losses compared to the optimal policy and is better approximated by core rather than headline inflation targeting. An even better approximation of the CONDI can be obtained with an adjusted core index that covers total expenditures excluding autos, clothing, energy, and food at home, but that includes food away from home.