  Let ${\mathcal C}= \bigcup_{i=1}^n C_i \subseteq \mathbb{P}^2$ be a
collection of smooth rational plane curves. We prove that the addition-deletion
operation used in the study of hyperplane arrangements has an extension which
works for a large class of arrangements of smooth rational curves, giving an
inductive tool for understanding the freeness of the module $\Omega^1({\mathcal
C})$ of logarithmic differential forms with pole along ${\mathcal C}$. We also
show that the analog of Terao's conjecture (freeness of $\Omega^1({\mathcal
C})$ is combinatorially determined if ${\mathcal C}$ is a union of lines) is
false in this setting.
