We show that a separable purely infinite C ∗ -algebra is of real rank zero if and only if its primitive ideal space has a basis consisting of compact-open sets and the natural map K0(I) → K0(I/J) is surjective for all closed two-sided ideals J ⊂ I in the C ∗ -algebra. It follows in particular that if A is any separable C ∗ -algebra, then A ⊗ O2 is of real rank zero if and only if the primitive ideal space of A has a basis of compact-open sets, which again happens if and only if A⊗O2 has the ideal property. This is joint work with Mikael Rørdam (to appear in J. Reine Angew. Math.).