Theorem A. Let $T$ be a small superstable theory, $A$ a finite set, and $\psi$ a weakly minimal formula over $A$ which is contained in some nontrivial type which does not have Morley rank. Then $\psi$ is contained in some nonalgebraic isolated type over $A$. As an application we prove Theorem B. Suppose that $T$ is small and superstable, $A$ is finite, and there is a nontrivial weakly minimal type $p \in S(A)$ which does not have Morley rank. Then the prime model over $A$ is not minimal over $A$.