  We establish a coloring theorem for successors of a singular cardinals, and
use it prove that for any such cardinal $\mu$, we have
$\mu^+\nrightarrow[\mu^+]^2_{\mu^+}$ if and only if
$\mu^+\nrightarrow[\mu^+]^2_{\theta}$ for arbitrarily large $\theta<\mu$.
