Exhaust emissions resulting from the combustion of hydrocarbon fuels in compression ignition engines may be reduced using a homopolymer that may be polyisobutylene, polypropylene, and/or hyperbranched polyalpha-olefins. The homopolymer may have a molecular weight of from about 1600 to about 275,000. Optionally, an alkyl nitrate such as 2-ethylhexylnitrate (2EHN), and/or a peroxide, such as hydrogen peroxide, may also be used together with the homopolymer. Both NOx and particulate matter emissions (PM) may be reduced using ppm quantities of the additive compositions; alternatively, NOx emissions may be lowered or reduced while PM emissions do not substantially increase.