Stable block copolymer micelles with crosslinked rubbery cores serve as model soft colloids with tunable rheology. We demonstrate this by studying systematically two such micelles: one with a small polyisoprene core and long polystyrene hairs that dominate the response of the system, and another with a larger polybutadiene core and shorter polystyrene hairs, exhibiting colloid-like behavior. In addition to mass concentration, we use temperature as a means to vary the volume fraction and show that achieving the same volume fraction by these two different routes yields different macroscopic properties. The number density of the particles and osmotic pressure effects are the origin of the difference. The response of these micelles to varying s...