NOVELTY - Diesel fuel additive composition comprises a diesel fuel additive having a number average molecular weight of 500-10000, and which is a hydrocarbyl-substituted acid or anhydride or its derivative, or a hydrocarbyl-substituted Mannich base, where the additive has a molecular weight distribution so that less than 25 wt.% of the additive has a molecular weight of less than or equal to 400 as measured by gel permeation chromatography (GPC) based on a polystyrene calibration curve.    USE - The diesel fuel additive composition is useful in an ultra-low sulfur diesel fuel, which is useful in a high pressure diesel fuel injection system in a diesel engine having injectors, and for combusting a diesel fuel containing 15 or less ppm by weight of sulfur (all claimed).    ADVANTAGE - The diesel fuel additives: provide improved injector performance with the reduced deposits and injector sticking in high pressure diesel fuel injection system; and have improved stability.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for improving a fuel additive for an ultra-low sulfur diesel fuel in order to reduce deposits and injector sticking in high pressure diesel fuel injection system for a diesel engine, comprising: charging a hydrocarbyl component to a reaction vessel; vacuum distilling the hydrocarbyl component at 200 degrees C for a period of time sufficient to remove at least a portion of the hydrocarbyl component, a distillation residue of the distilled hydrocarbyl component is effective to provide the diesel fuel additive; reacting the distillation residue with a component comprising unsaturated dicarboxylic acid or anhydride and a phenol or substituted phenol to provide a hydrocarbyl-substituted component; and reacting the hydrocarbyl-substituted component with an amine or amine plus aldehyde to provide the additive comprising a hydrocarbyl-substituted succinic acid or anhydride imide and a hydrocarbyl-substituted Mannich base having a number average molecular weight of 500-10000.