Let $f_{0}:X_{0}\rightarrow B_{0}$ be as in Theorem 2.1, and $f:X\rightarrow B$ the compactification produced in the proof of Theorem 2.1. Then if $B$ is simply connected and $H^{0}(B,R^{1}f_{*}{\bf Z}/n{\bf Z})=0$ for all $n$, then $X$ is simply connected.