Theorem A. Let $M$ be a left $R$-module such that $\mathrm{Th}(M)$ is small and weakly minimal, but does not have Morley rank 1. Let $A = \mathrm{acl}(\varnothing) \cap M$ and $I = \{r \in R: rM \subset A\}$. Notice that $I$ is an ideal. (i) $F = R/I$ is a finite field. (ii) Suppose that $a, b_0,\ldots,b_n \in M$ and $a \bar{b}$. Then there are $s, r_i \in R, i \leq n$, such that $sa + \sum_{i \leq n} r_ib_i \in A$ and $s \not\in I$. It follows from Theorem A that algebraic closure in $M$ is modular. Using this and results in [B1] and [B2], we obtain Theorem B. Let $M$ be as in Theorem A. Then Vaught's conjecture holds for $\mathrm{Th}(M)$.