I painted the white fur like I usually do, with a gray undercoat then working up slowly through grays and beiges to white.
But I tried something different for the red fur. I worked a small section at a time, beginning with the parts farther from the viewer and working forward. For each section, I undercoated with white then immediately came back - with a very light touch - into the wet white paint with the transaparent colors. They mixed and blended with the white on the canvas to create a smooth light colored base. Then when the base dried I put layers of transparent fur strokes with the colors. This method worked pretty well.
I also tried to be more dramatic than I usually am with the values, and I need to do this more often.