The filling-in theory of brightness perception has gained much attention recently owing to the success of vision models. However, the theory and its instantiations have suffered from incorrectly dealing with transitive brightness relations. This paper describes an advance in the filling-in theory that overcomes the problem. The advance is incorporated into the BCS/FCS neural network model, which allows it, for the first time, to account for all of Arend's test stimuli for assessing brightness perception models. The theory also suggests a new teleology for parallel ON- and OFF-channels.