Both hair rendering and global illumination are known to be computationally expensive, and for this reason we see very few examples using global illumination techniques in hair rendering. In this paper, we elaborate on different simplification approaches to allow practical global illumination solutions for high quality hair rendering. We categorize light paths of a full global illumination solution, and analyze their costs and illumination contributions both theoretically and experimentally. We also propose two different implementation techniques using our novel projection based indirect illumination computation approach and state of the art ray tracing for hair. Our results show that by using our simplifications, a global illumination solution for hair is practical.