Can a Bose gas be saturated?

We scrutinize the concept of saturation of the thermal component in a partially condensed trapped Bose gas. Using a 39K gas with tunable interactions, we demonstrate strong deviation from Einstein's textbook concept of a saturated vapor. However, the saturation picture can be recovered by extrapolation to the strictly noninteracting limit. We provide evidence for the universality of our observations through additional measurements with a different atomic species, 87Rb.