Shipping is a growing sector in the global economy and it contributions to global CO2 emissions are expected to increase. CO2 emissions from the world shipping fleet will likely be regulated in the near future, and studies have shown that significant emission reductions can be achieved at low cost. Regulations are being discussed for both existing ships, as well as for future additions to the fleet. In this study a plausible CO2 emission reduction inventory is constructed for the cargo fleet existing in 2010, as well as for container ships, bulk ships and tankers separately. In the reduction inventories CO2 emissions are reduced by 25-32% relative to baseline by a ship type specific cost-effectiveness criterion, and 9 other emission compounds are changed as a technical implication of reducing CO2. The overall climate and environmental effects of the changes to all 10 emission components in the reduction inventory are assessed using a chemical transport model, radiative forcing (RF) models and a simple climate model. We find substantial environmental and health benefits with up to 5% reduction in surface ozone levels, 15% reductions in surface sulfate and 10% reductions in wet deposition of sulfate in certain regions exposed to heavy ship traffic. The major ship types show distinctly different contributions in specific locations. For instance, the container fleet contributes 50% of the sulfate decline on the west coast of North America. The global radiative forcing from a 1-yr emission equal to the difference between baseline and reduction inventory, show an initial strong positive forcing from non-CO2 compounds. This warming effect is due to reduced cooling by aerosols and methane. After approximately 25 yr, the non-CO2 forcing is balanced by the CO2 forcing. For the global mean temperature change we find a shift from warming to cooling after approximately 60 yr. The major ship types show significant differences in the short term radiative forcing; for instance the direct SO4 forcing from tankers is 30% higher than for container and bulk. The net long term effects on RF are similar due to similar CO2 forcing. We assess an emission scenario where the reduction inventory is sustained on the fleet as it steadily diminishes over time due to scrapping and disappears in 2040. We find a net temperature increase lasting until approximately 2080. We conclude that changes in non-CO2 emission does matter significantly if reductions of CO2 emissions are made on the year 2010 cargo shipping fleet. In sum, we find that emission changes motivated by CO2 reductions in shipping will be beneficial from a long-term climate perspective, and there are also positive environmental and health effects identified as concentrations of key short-lived pollutants are reduced.