NOVELTY - Renewable high-efficiency (RHE) diesel fuel comprises: a high paraffin diesel comprising hydrotreated triglycerides including tallow or vegetable oil; and/or esters, ethers and/or hemiacetals comprising alcohols and/or polyols.    USE - The RHE-diesel fuel is useful for reducing the emissions of a diesel engine (claimed).    ADVANTAGE - The RHE-diesel fuel has: a cetane number of greater than that of conventional diesel fuel, including a cetane number of 51-81, and a high efficiency diesel fuel with a derived cetane number of 60, 65, 70, 75, 80, 45-51, 51-81, or above 81, or greater than 85; a combustion efficiency of 98.19-98.69%, reduced nitrogen oxide (NOx) emissions of 0.63-2.01 g/kg-fuel, reduced particulate matter emissions of 0.45-0.71 g/kg-fuel, reduced total hydrocarbon emissions of 2.01-3.69 g/kg-fuel, and reduced carbon monoxide emissions of 8.62-13.98 g/kg-fuel; an increase in brake thermal efficiency of greater than 1%, preferably at least 1.5%, compared to an identical method where the fuel is a conventional diesel fuel; a decrease in nitrogen oxide (NOx) emissions of greater than 10%, preferably greater than or equal to 20%, compared to an identical method where the fuel is a diesel fuel; a decrease in particulate matter emissions of greater than 55%, preferably greater than or equal to 70%, compared to an identical method where the fuel is a diesel fuel; a decrease in total hydrocarbon emissions of greater than 75%, preferably greater than or equal to 90%, compared to an identical method where the fuel is a diesel fuel; and/or a decrease in carbon monoxide emissions of greater than 70%, preferably greater than or equal to 80%, compared to an identical method where the fuel is a diesel fuel. The RHE-diesel fuel reduces pollution because of the increase combustion efficiency, lower emissions, and ability to use a wider range of fuel sources.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for reducing the emissions of a diesel engine, comprising combusting the RHE-diesel fuel that is injected at -8 to 0 degrees after top dead center, and operating the engine with an exhaust gas recirculation of 20-60%.