Iapetus is Saturn's third largest moon, and its most strange, having a two-tone coloration, an equatorial mountain ridge and squashed poles. The moon's density shows it is only one-fifth rock, the rest being water ice. Its surface gravity is just 2.29% of Earth's. It may be more practical to paraterraform this strange moon.
To terraform Iapetus, the surface ices would have to be artificially heated by an orbiting ring of fusion satellites to create a thin atmosphere. Then, Sulfur Hexaflouride, Nitrogen Triflouride and other greenhouse gases could be added to heat up the water-ice on the moon until it begins to thaw out. Nitrogen could be produced in two ways: by transferring some of Titan's atmosphere to Iapetus, and by introducing bacteria that break down compounds already present on Iapetus (like ammonia) into nitrogen gas. The dark surface of Iapetus is covered with Hydrogen cyanide , a poisonous substance which would need to be removed or broken down. Next, through electrolysis of the forming oceans, oxygen would be produced for the atmosphere. The surface, being mainly ice, would completely melt into a deep ocean without any landforms at all, so Artificial Continents would need to be built and topped with Earth-like soil. The equatorial mountain range would unfortunately be destroyed in the process of terraforming. However, to content the tourists, it could be remade into a chain of floating resorts.
See also: Iapetus Simulation.