For Tychonoff $X$ and $\alpha$ an infinite cardinal, let $\alpha defX:=$ the minimum number of $\alpha$ cozero-sets of the Čech-Stone compactification which intersect to $X$ (generalizing $ℝ$-defect), and let $rtX:={min}_{\alpha }max(\alpha ,\alpha defX)$. Give $C\left(X\right)$ the compact-open topology. It is shown that $\tau C\left(X\right)\le n\chi C\left(X\right)\le rtX=max\left(L\right(X),L(X)defX)$, where: $\tau$ is tightness; $n\chi$ is the network character; $L\left(X\right)$ is the Lindel"of number. For example, it follows that, for $X$ Čech-complete, $\tau C\left(X\right)=L\left(X\right)$. The (apparently new) cardinal functions $n\chi C$ and $rt$ are compared with several others.