Summary: Like Lorenz curve, the cumulated mean income curve (COMIC) can also be used as a measure of income inequality. The present paper considers the asymptotic variance-covariance structure of the COMIC ordinates at some pre-selected points. Asymptotically nonparametric joint confidence intervals for COMIC ordinates are derived. Testing for COMIC dominance is carried out through two different approaches and a comparison of these two testing procedures is done by comparing their corresponding powers. A real life illustration is included.