Let $T$ be superstable. We say a type $p$ is weakly minimal if $R(p, L, \infty) = 1$. Let $M \models T$ be uncountable and saturated, $H = p(M)$. We say $D \subset H$ is locally modular if for all $X, Y \subset D$ with $X = \operatorname{acl}(X) \cap D, Y = \operatorname{acl}(Y) \cap D$ and $X \cap Y \neq \varnothing$, $\dim(X \cup Y) + \dim(X \cap Y) = \dim(X) + \dim(Y)$. Theorem 1. Let $p \in S(A)$ be weakly minimal and $D$ the realizations of $\operatorname{stp}(a/A)$ for some a realizing $p$. Then $D$ is locally modular or $p$ has Morley rank 1. Theorem 2. Let $H, G$ be definable over some finite $A$, weakly minimal, locally modular and nonorthogonal. Then for all $a \in H\backslash\operatorname{acl}(A), b \in G\operatorname{acl}(A)$ there are $a' \in H, b' \in G$ such that $a' \in \operatorname{acl}(abb' A)\backslash\operatorname{acl}(aA)$. Similarly when $H$ and $G$ are the realizations of complete types or strong types over $A$.