We construct a price index with weights for the prices of different PCE (personal consumption expenditures) goods chosen to minimize the welfare costs of nominal distortions. In this cost-of-nominal-distortions index (CONDI), the weights are computed in a multi-sector New Keynesian model with time-dependent price setting. The model is calibrated using U.S. data on the dispersion of price stickiness and labor shares across sectors. We find that the CONDI weights depend mostly on price stickiness and are less affected by the dispersion in labor shares. Moreover, CONDI stabilization closely approximates the optimal monetary policy and leads to negligible welfare losses. Finally, CONDI is better approximated by targeting core inflation rather than headline inflation - and is even better approximated with an adjusted core index that covers total expenditures excluding autos, clothing, energy, and food at home, but including food away from home.