My little rice cooker has two settings: Cook and Warm. I start with a 3:1 ratio of water:rice. Once the cooker auto-switches from Cook to Warm, I add more water (about as much as the original dry amount of rice), and leave it on the warm setting 'til the water evaporates, then unplug the cooker. This makes the rice a bit gooeyer, but not fatty.
For fat, to me, the only thing that tastes better on rice than butter and salt is (maybe) a hunk of salmon.