In this paper we establish the following theorems. THEOREM A. Let $T$ be a complete first-order theory which is uncountable. Then: (i) $I(|T|, T) \geq \aleph_0$. (ii) If $T$ is not unidimensional, then for any $\lambda \geq |T|, I (\lambda, T) \geq \aleph_0$. THEOREM B. Let $T$ be superstable, not totally transcendental and nonmultidimensional. Let $\theta(x)$ be a formula of least $R^\infty$ rank which does not have Morley rank, and let $p$ be any stationary completion of $\theta$ which also fails to have Morley rank. Then $p$ is regular and locally modular.